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Fri, Jun 29, '18
14:00 - 15:00
CRiSM Seminar
D1.07
Fri, Jun 15, '18
14:00 - 15:00
CRiSM Seminar
D1.07
Fri, Jun 1, '18
14:00 - 15:00
CRiSM Seminar
D1.07
Fri, May 18, '18
14:00 - 15:00
CRiSM Seminar
D1.07
Fri, May 4, '18
14:00 - 15:00
CRiSM Seminar
D1.07
Fri, Mar 16, '18
14:00 - 15:00
CRiSM Seminar
MA_B1.01
Fri, Mar 2, '18
14:00 - 15:00
CRiSM Seminar
MA_B1.01
Fri, Feb 16, '18
14:00 - 15:00
CRiSM Seminar
MA_B1.01
Fri, Feb 2, '18
14:00 - 15:00
CRiSM Seminar
MA_B1.01
Fri, Jan 19, '18
14:00 - 15:00
CRiSM Seminar
MA_B1.01
Fri, Dec 8, '17
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Nov 24, '17
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Nov 10, '17
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Oct 27, '17
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Oct 13, '17
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Jun 30, '17
14:00 - 15:00
CRiSM Seminar - Paul Kirk (BSU, Cambridge) (C1.06)
C1.06, Zeeman Building

Title: Semi-supervised multiview clustering for high-dimensional data

Abstract: Although the challenges presented by high dimensional data in the context of regression are well-known and the subject of much current research, comparatively little work has been done on this in the context of clustering. In this setting, the key challenge is that often only a small subset of the covariates provides a relevant stratification of the population. Identifying relevant strata can be particularly challenging when dealing with high-dimensional datasets, in which there may be many covariates that provide no information whatsoever about population structure, or – perhaps worse – in which there may be (potentially large) covariate subsets that define irrelevant stratifications. For example, when dealing with genetic data, there may be some genetic variants that allow us to group patients in terms of disease risk, but others that would provide completely irrelevant stratifications (e.g. which would group patients together on the basis of eye or hair colour). Bayesian profile regression is a semi-supervised model-based clustering approach that makes use of a response in order to guide the clustering toward relevant stratifications. Here we consider how this approach can be extended to the "multiview" setting, in which different groups of covariates ("views") define different stratifications. We also present a heuristic alternative, some preliminary results in the context of breast cancer subtyping, and consider how the approach could also be used to integrate different 'omics datasets (assuming that each dataset provides measurements on a common set of individuals).

Fri, May 19, '17
14:00 - 15:00
CRiSM Seminar
D1.07

Korbinian Strimmer (Imperial)

An entropy approach for integrative genomics and network modeling

Multivariate regression approaches such as Seemingly Unrelated Regression (SUR) or Partial Least Squares (PLS) are commonly used in vertical data integration to jointly analyse different types of omics data measured on the same samples, such as SNP and gene expression data (eQTL) or proteomic and transcriptomic data.  However, these approaches may be difficult to apply and to interpret for computational and conceptual reasons.

Here we present a simple alternative approach to integrative genomics based on using relative entropy to characterise the overall association between two (or more) sets of omic data, and to infer the underlying corresponding association network among the individual covariates.  This approach is computationally inexpensive and can be applied to large-dimensional data sets.  A key and novel feature of our method is decomposition of the total strength between two or more groups of variables based on optimal whitening of the individual data sets.  Correspondingly, it may also be viewed as a special form of a latent-variable multivariate regression model.

We illustrate this approach by analysing metabolomic and transcriptomic data from the DILGOM study.


References:

A. Kessy, A. Lewin, and K. Strimmer. 2017. Optimal whitening and decorrelation. The American Statistician, to appear. http://dx.doi.org/10.1080/00031305.2016.1277159
T. Jendoubi and K. Strimmer. 2017. Data integration and network modeling: an entropy approach.  In prep.
Fri, May 5, '17
14:00 - 15:00
CRiSM Seminar
D1.07

"Adaptive MCMC For Everyone"

Jeffrey Rosenthal, University of Toronto

Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis
Algorithm and the Gibbs Sampler, are an extremely useful
and popular method of approximately sampling from complicated
probability distributions. Adaptive MCMC attempts to automatically
modify the algorithm while it runs, to improve its performance on
the fly. However, such adaptation often destroys the ergodicity
properties necessary for the algorithm to be valid. In this talk,
we first illustrate MCMC algorithms using simple graphical Java
applets. We then discuss adaptive MCMC, and present examples and
theorems concerning its ergodicity and efficiency. We close with
some recent ideas which make adaptive MCMC more widely applicable
in broader contexts.

Fri, Mar 17, '17
14:00 - 15:00
CRiSM Seminar
MA_B1.01

Paul Birrell (MRC Biostatistics Unit, Cambridge)

Towards Computationally Efficient Epidemic Inference

In a pandemic where infection is widespread, there is no direct observation of the infection processes. Instead information comes from a variety of surveillance data schemes that are prone to noise, contamination, bias and sparse sampling. To form an accurate impression of the epidemic and to be able to make forecasts of its evolution, therefore, as many of these data streams as possible need to be assimilated into a single integrated analysis. The result of this is that the transmission model describing the infection process and the linked observation models can become computationally demanding, limiting the capacity for statistical inference in real-time.

I will discuss some of our attempts at making the inferential process more efficient, with particular focus on dynamic emulation, where the computationally expensive epidemic model is replaced by a more readily evaluated proxy, a time-evolving Gaussian process trained on a (relatively) small number of model runs at key input values, training that can be done a priori.

 

Fri, Mar 3, '17
14:00 - 15:00
CRiSM Seminar
MA_B1.01

Marcelo Pereyra

Bayesian inference by convex optimisation: theory, methods, and algorithms.

Abstract:

Convex optimisation has become the main Bayesian computation methodology in many areas of data science such as mathematical imaging and machine learning, where high dimensionality is often addressed by using models that are log-concave and where maximum-a-posteriori (MAP) estimation can be performed efficiently by optimisation. The first part of this talk presents a new decision-theoretic derivation of MAP estimation and shows that, contrary to common belief, under log-concavity MAP estimators are proper Bayesian estimators. A main novelty is that the derivation is based on differential geometry. Following on from this, we establish universal theoretical guarantees for the estimation error involved and show estimation stability in high dimensions. Moreover, the second part of the talk describes a new general methodology for approximating Bayesian high-posterior-density regions in log-concave models. The approximations are derived by using recent concentration of measure results related to information theory, and can be computed very efficiently, even in large-scale problems, by using convex optimisation techniques. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is finally illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where they are used to explore the uncertainty about the solutions, and where convex-optimisation-empowered proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error.

Fri, Feb 17, '17
14:00 - 15:00
CRiSM Seminar
MA_B1.01

Ioannis Kosmidis

Title:
Reduced-bias inference for regression models with tractable and
intractable likelihoods

Abstract:

This talk focuses on a unified theoretical and algorithmic framework
for reducing bias in the estimation of statistical models from a
practitioners point of view. We will briefly discuss how shortcomings
of classical estimators and of inferential procedures depending on
those can be overcome via reduction of bias, and provide a few
demonstrations stemming from current and past research on well-used
statistical models with tractable likelihoods, including beta
regression for bounded-domain responses, and the typically
small-sample setting of meta-analysis and meta-regression in the
presence of heterogeneity. The large impact that bias in the
estimation of the variance components can have on inference motivates
delivering higher-order corrective methods for generalised linear
mixed models. The challenges in doing that will be presented along
with resolutions stemming from current research.
Fri, Feb 3, '17
14:00 - 15:00
CRiSM Seminar
MA_B1.01

Liz Ryan (KCL)

Title: Simulation-based Fully Bayesian Experimental Design

Abstract:

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of Bayesian algorithms, such as Markov chain Monte Carlo (MCMC) algorithms. However, many of the proposed algorithms have been found to be computationally intensive for complex or nonstandard design problems, such as those which require a large number of design points to be found and/or those for which the observed data likelihood has no analytic expression. In this work, we develop novel extensions of existing algorithms which have been used for Bayesian experimental design, and also incorporate methodologies which have been used for Bayesian inference into the design framework, so that solutions to more complex design problems can be found.

Fri, Jan 20, '17
14:00 - 15:00
CRiSM Seminar
MA_B1.01

Yi Yu (University of Bristol)

Title: Estimating whole brain dynamics using spectral clustering

Abstract: The estimation of time-varying networks for functional Magnetic Resonance Imaging (fMRI) data sets is of increasing importance and interest. In this work, we formulate the problem in a high-dimensional time series framework and introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. NCPD is applied to various simulated data and a resting-state fMRI data set. This new methodology also allows us to identify common functional states within and across subjects. Finally, NCPD promises to offer a deep insight into the large-scale characterisations and dynamics of the brain. This is joint work with Ivor Cribben (Alberta School of Business).

Fri, Dec 9, '16
15:00 - 16:00
CRiSM Seminar
A1.01

Satish Iyengar - Big Data Challenges in Psychiatry

 Current psychiatric diagnoses are based primarily on self-reported experiences. Unfortu- nately, treatments for the diagnoses are not effective for all patients. One hypothesized reason is that “artificial grouping of heterogeneous syndromes with different pathophysio- logical mechanisms into one disorder.” To address this problem, the US National Institute of Mental Health instituted the Research Domain Criteria framework in 2009. This re- search framework calls for integrating data from many levels of information: genes, cells, molecules, circuits, physiology, behavior, and self-report. Clustering comes to the forefront as a key tool in this big-data effort. In this talk, we present a case study of the use of mix- ture models to cluster older adults based on measures of sleep from three domains: diary, actigraphy, and polysomnography. Challenges in this effort include the use of mixtures of asymmetric (skewed) distributions, a large number of potential clustering variables, and seeking clinically meaningful solutions. We present novel variable selection algorithms, study them by simulation, and demonstrate our methods on the sleep data. This work is joint with Dr. Meredith Wallace.

 

Fri, Nov 25, '16
15:00 - 16:00
CRiSM Seminar
A1.01
Fri, Nov 11, '16
15:00 - 16:00
CRiSM Seminar
A1.01

Mingli Chen

Fri, Oct 28, '16
15:00 - 16:00
CRiSM Seminar
A1.01

Peter Orbanz

Fri, Oct 14, '16
15:00 - 16:00
CRiSM Seminar
A1.01

Daniel Rudolf - Perturbation theory for Markov chains

Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. Under a convergence condition we present an estimate of the Wasserstein distance of the nth step distributions between an ideal, unperturbed and an approximating, perturbed Markov chain. We illustrate the result with an example of an autoregressive process.

 

Tue, Aug 30, '16
CRiSM Master Class on Sparse Regression
MS.01

Runs from Tuesday, August 30 to Thursday, September 01.

Fri, Jul 1, '16
14:00 - 17:00
CRiSM Seminar
D1.07

Gonzalo Garcia Donato (Universidad Castilla La Mancha)

Criteria for Bayesian model choice

In model choice (or model selection) several statistical models are postulated as legitimate explanations for a response variable and this uncertainty is to be propagated in the inferential process. The type of questions one is aimed to answer is assorted ranging from e.g. identifying the `true’ model to produce more reliable estimates that takes into account this extra source of variability. Particular important problems of model choice are hypothesis testing, model averaging and variable selection. The Bayesian paradigm provides a conceptually simple and unified solution to the model selection problem: the posterior probabilities of the competing models. This is also named the posterior distribution over the model space and is a simple function of Bayes factors. Answering any question of interest just reduces to summarizing properly this posterior distribution.

Unfortunately, the posterior distribution may depend dramatically on the prior inputs and unlike estimation problems (where model is fixed) such sensitivity does not vanish with large sample sizes. Additionally, it is well known that standard solutions like improper or vague priors cannot be used in general as they result in arbitrary Bayes factors. Bayarri et al (2012) propose tackling these difficulties basing the assignment of prior distributions in objective contexts on a number of sensible statistical. This approach takes a step beyond a way of analyzing the problem that Jeffreys inaugurated fifty years ago.

In this talk the criteria will be presented with emphasis on those aspects who serve to characterize features of the priors that, until today, have been popularly used without a clear justification.

Originally the criteria were accompanied with an application to variable selection in regression models and here we will see how they can be useful to tackle other important scenarios like high dimensional settings or survival problems.

Fri, Jun 17, '16
14:00 - 17:00
CRiSM Seminar
D1.07

 

Fri, Jun 10, '16
14:00 - 17:00
CRiSM Seminar

Claire Gormley (University College Dublin)

Clustering High Dimensional Mixed Data: Joint Analysis of Phenotypic and Genotypic Data

The LIPGENE-SU.VI.MAX study, like many others, recorded high dimensional continuous phenotypic data and categorical genotypic data. Interest lies in clustering the study participant into homogeneous groups or sub-phenotypes, by jointly considering their phenotypic and genotypic data, and in determining which variables are discriminatory.

A novel latent variable model which elegantly accommodates high dimensional, mixed data is developed to cluster participants using a Bayesian finite mixture model. A computationally efficient variable selection algorithm is incorporated, estimation is via a Gibbs sampling algorithm and an approximate BIC-MCMC criterion is developed to select the optimal model.

Two clusters or sub-phenotypes (‘healthy’ and ‘at risk’) are uncovered. A small subset of variables is deemed discriminatory which notably includes phenotypic and genotypic variables, highlighting the need to jointly consider both factors. Further, seven years after the data were collected, participants underwent further analysis to diagnose presence or absence of the metabolic syndrome (MetS). The two uncovered sub-phenotypes strongly correspond to the seven year follow up disease classification, highlighting the role of phenotypic and genotypic factors in the MetS, and emphasising the potential utility of the clustering approach in early screening. Additionally, the ability of the proposed approach to define the uncertainty in sub-phenotype membership at the participant level is synonymous with the concepts of precision medicine and nutrition.

Fri, Jun 3, '16
14:00 - 17:00
CRiSM Seminar
D1.07

Degui Li (University of York)

Panel Data Models with Interactive Fixed Effects and Multiple Structural Breaks

In this paper we consider estimation of common structural breaks in panel data models with interactive fixed effects which are unobservable. We introduce a penalized principal component (PPC) estimation procedure with an adaptive group fused LASSO to detect the multiple structural breaks in the models. Under some mild conditions, we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates. furthermore, we estimate the regression coefficients through the post-LASSO method and establish the asymptotic distrbution theory for the resulting estimators. The developed methodology and theory are applicable to the case of dynamic panel data models. The Monte Carlo simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist. We finally apply our method to study the environmental Kuznets curve for 74 countries over 40 years and detect two breaks in the data.

Fri, May 20, '16
14:00 - 17:00
CRiSM Seminar
D1.07

Jon Forster (Southampton)

Model integration for mortality estimation and forecasting

The decennial English Life Tables have been produced after every UK decennial census since 1841. They are based on graduated (smoothed) estimates of central mortality rates, or related functions. For UK mortality, over the majority of the age range, a GAM can provide a smooth function which adheres acceptably well to the crude mortality rates. At the very highest ages, the sparsity of the data mean that the uncertainty about mortality rates is much greater. A further issue is that life table estimation requires us to extrapolate the estimate of the mortality rate function to ages beyond the extremes of the observed data. Our approach integrates a GAM at lower ages with a low-dimensional parametric model at higher ages. Uncertainty about the threshold age ,at which the transition to the simpler model occurs, is integrated into the analysis.

This base structure can then be extended into a model for the evolution of mortality rates over time, allowing the forecasting of mortality rates, a key input into demographic projections necessary for planning.

Fri, May 13, '16
14:00 - 17:00
CRiSM Seminar
B1.01

Michael Newton (University of Wisconsin-Madison)

Ranking and selection revisited

In large-scale inference the precision with which individual parameters are estimated may vary greatly among parameters, thus complicating the task to rank order parameters. I present a framework for evaluating different ranking/selection schemes as well as an empirical Bayesian methodology showing theoretical and empirical advantages over available approaches. Examples from genomics and sports will help to illustrate the issues.

Fri, May 6, '16
14:00 - 17:00
CRiSM Seminar
MS.03

Mikhail Malyutov (Northeastern University)

Context-free and Grammer-free Statistical Testing Identity of Styles

Our theory justifies our thorough statistical modification CCC of D.Khmelev's conditional compression based classification idea of 2001 and the 7 years of intensive applied statistical implementation of CCC for authorship attribution of literary works.

Homogeneity testing based on SCOT training with applications to the financial modeling and Statistical Quality Control are also in progress. Both approaches are desrcibed in a Springer monograph which appears shortly. Stochastic Context Tree (abbreviated as SCOT) is m-Markov Chain with every state of a spring independent of the symbols in its more remote past than the context of length determined by the preceding symbols of this state.

In all of our applications we uncover a complex sparse structure of memory in SCOT models that allows excellent discrimination power. In additiion, a straightforward estimation of the stationary distributio of SCOT gives insight into contexts crucial for discrimination between, say, different regimes of financial data or between styles of different authors of literary tests.

Mon, Apr 4, '16
CRiSM Master Class: Non-Parametric Bayes
MS.01

Runs from Monday, April 04 to Friday, April 08.

Fri, Mar 18, '16
14:00 - 15:00
CRiSM Seminar
B1.01

Petros Dellaporta (UCL)

Scalable inference for a full multivariate stochastic volatility model

Abstract: We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of assets is prohibitively large, we propose a factor multivariate stochastic volatility model in which the variances and correlations of the factors evolve stochastically over time. Inference is achieved via a carefully designed feasible andscalable Markov chain Monte Carlo algorithm that combines two computationally important ingredients: it utilizes invariant to the prior Metropolis proposal densities for simultaneously updating all latent paths and has quadratic, rather than cubic, computational complexity when evaluating the multivariate normal densities required. We apply our modelling and computational methodology to 571 stock daily returns of Euro STOXX index for data over a period of 10 years.

Fri, Mar 4, '16
14:00 - 15:00
CRiSM Seminar
B1.01

Alan Gelfand (Duke, Dept of Statistical Science)

Title: Space and circular time log Gaussian Cox processes with application to crime event data

Abstract: We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Poisson process or with a more general Cox process, we need to specify a space-time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. In fact, we view time as circular, necessitating valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. In addition, crimes are classified by crime type.

Furthermore, each crime event is marked by day of the year which we convert to day of the week. We present models to accommodate such data. Then, we extend the modeling to include the marks. Our specifications naturally take the form of hierarchical models which we t within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare separable vs. nonseparable covariance specifications. 

Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012. Again, we have location, hour, day of the year, and crime type for each event. We investigate a rich range

of models to enhance our understanding of the set of incidences.

Fri, Feb 19, '16
14:00 - 15:00
CRiSM Seminar
B1.01

Theresa Smith (CHICAS, Lancaster Medical School)

Modelling geo-located health data using spatio-temporal log-Gaussian Cox processes

Abstract: Health data with high spatial and temporal resolution are becoming more common, but there are several practical and computational challenges to using such data to study the relationships between disease risk and possible predictors. These difficulties include lack of measurements on individual-level covariates/exposures, integrating data measured on difference spatial and temporal units, and computational complexity.

In this talk, I outline strategies for jointly estimating systematic (i.e., parametric) trends in disease risk and assessing residual risk with spatio-temporal log-Gaussian Cox processes (LGCPs). In particular, I will present a Bayesian methods and MCMC tools for using spatio-temporal LGCPs to investigate the roles of environmental and socio-economic risk-factors in the incidence of Campylobacter in England.

 

 

Fri, Feb 5, '16
14:00 - 15:00
CRiSM Seminar
B1.01

Ewan Cameron (Oxford, Dept of Zoology)

Progress and (Statistical) Challenges in Malariology

Abstract: In this talk I will describe some key statistical challenges faced by researchers aiming to quantify the burden of disease arising from Plasmodium falciparum malaria at the population level. These include covariate selection in the 'big data' setting, handling spatially-correlated residuals at scale, calibration of individual simulation models of disease transmission, and the embedding of continuous-time, discrete-state Markov Chain solutions within hierarchical Bayesian models. In each case I will describe the pragmatic solutions we've implemented to-date within the Malaria Atlas Project, and highlight more sophisticated solutions we'd like to have in the near-future if the right statistical methodology and computational tools can be identified and/or developed to this end.

References:

http://www.nature.com/nature/journal/v526/n7572/abs/nature15535.html

http://www.nature.com/ncomms/2015/150907/ncomms9170/full/ncomms9170.html

http://www.ncbi.nlm.nih.gov/pubmed/25890035

http://link.springer.com/article/10.1186/s12936-015-0984-9

 

Fri, Jan 22, '16
14:00 - 15:00
CRiSM Seminar
B1.01

Li Su with Michael J. Daniels (MRC Biostatistics Unit)
Bayesian modeling of the covariance structure for irregular longitudinal data using the partial autocorrelation function
Abstract: In long-term follow-up studies, irregular longitudinal data are observed when individuals are assessed repeatedly over time but at uncommon and irregularly spaced time points. Modeling the covariance structure for this type of data is challenging, as it requires specification of a covariance function that is positive definite. Moreover, in certain settings, careful modeling of the covariance structure for irregular longitudinal data can be crucial in order to ensure no bias arises in the mean structure. Two common settings where this occurs are studies with ‘outcome-dependent follow-up’ and studies with ‘ignorable missing data’. ‘Outcome-dependent follow-up’ occurs when individuals with a history of poor health outcomes had more follow-up measurements, and the intervals between the repeated measurements were shorter. When the follow-up time process only depends on previous outcomes, likelihood-based methods can still provide consistent estimates of the regression parameters, given that both the mean and covariance structures of the irregular longitudinal data are correctly specified and no model for the follow-up time process is required. For ‘ignorable missing data’, the missing data mechanism does not need to be specified, but valid likelihood-based inference requires correct specification of the covariance structure. In both cases, flexible modeling approaches for the covariance structure are essential. In this work*, we develop a flexible approach to modeling the covariance structure for irregular continuous longitudinal data using the partial autocorrelation function and the variance function. In particular, we propose semiparametric non-stationary partial autocorrelation function models, which do not suffer from complex positive definiteness restrictions like the autocorrelation function. We describe a Bayesian approach, discuss computational issues, and apply the proposed methods to CD4 count data from a pediatric AIDS clinical trial.
*Details can be found in the paper published in Statistics in Medicine 2015, 34, 2004–2018.

Thu, Dec 10, '15
14:00 - 15:00
CRiSM Seminar - Martin Lindquist (John Hopkins University, Dept of Biostatistics))
A1.01

Martin Lindquist (John Hopkins University, Dept of Biostatistics)

New Approaches towards High-dimensional Mediation

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the path between a randomized treatment and an outcome variable. The influence of the intermediate variable (mediator) on the outcome is often determined using structural equation models (SEMs). While there has been significant research on the topic in recent years, little is known about mediation analysis when the mediator is high dimensional. Here we discuss two approaches towards addressing this problem. The first is an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous function rather than a single scalar measure. The second finds the linear combination of a high-dimensional vector of potential mediators that maximizes the likelihood of the SEM. Both methods are applied to data from a functional magnetic resonance imaging (fMRI) study of thermal pain that sought to determine whether brain activation mediated the effect of applied temperature on self-reported pain.

Thu, Nov 26, '15
14:00 - 15:00
CRiSM Seminar - Ismael Castillo (Universite Paris 6, Laboratoire de Probabilites et Modeles Aleatoires
A1.01

Ismael Castillo (Université Paris 6, Laboratoire de Probabilités et Modèles Aléatoires)
On some properties of Polya trees posterior distributions

In Bayesian nonparametrics, Polya tree distributions form a popular and flexible class of priors on distributions or density functions. In the problem of density estimation, for certain choices of parameters, Polya trees have been shown to produce asymptotically consistent posterior distributions in a Hellinger sense. In this talk, after reviewing some general properties of Polya trees, I will show that the previous consistency result can be made much more precise in two directions: 1) rates of convergence can be derived 2) it is possible to characterise the limiting shape of the posterior distribution in a functional sense. We will discuss a few applications to Donsker-type results on the cumulative distribution function and to the study of some functionals of the density.
 

Thu, Nov 12, '15
14:00 - 15:00
CRiSM Seminar - Patrick Wolfe (UCL, Dept of Statistics Science))
A1.01

Patrick Wolfe (UCL, Dept of Statistical Science)
Network Analysis and Nonparametric Statistics

Networks are ubiquitous in today's world. Any time we make observations about people, places, or things and the interactions between them, we have a network. Yet a quantitative understanding of real-world networks is in its infancy, and must be based on strong theoretical and methodological foundations. The goal of this talk is to provide some insight into these foundations from the perspective of nonparametric statistics, in particular how trade-offs between model complexity and parsimony can be balanced to yield practical algorithms with provable properties.

Mon, Oct 26, '15
16:00 - 17:00
CRiSM Seminar - Hernando Ombao (UC Irvine, Dept of Statistics))
A1.01

Hernando Ombao (UC Irvine, Dept of Statistics)
Problems in Non-Stationary Multivariate Time Series With Applications in Brain Signals

We present new tools for analyzing complex multichannel signals using spectral methods. The key challenges are the high dimensionality of brain signals, massive size and the complex nature of the underlying physiological process – in particular, non-stationarity. In this talk, I will highlight some of the current projects. The first is a tool that identifies changes in the structure of a multivariate time series. This is motivated by problems in characterizing changes in brain signals during an epileptic seizure where a localized population of neurons

exhibits abnormal firing behavior which then spreads to other subpopulations of neurons. This abnormal firing behavior is captured by increases in signal amplitudes (which can be easily spotted by visual inspection) and changes in the decomposition of the waveforms and in the strength of dependence between different regions (which are more subtle). The proposed frequency-specific change-point detection method (FreSpeD) uses a cumulative sum test statistic within a binary segmentation algorithm. Theoretical optimal properties of the FreSpeD method will be developed. We demonstrate that, when applied to an epileptic seizure EEG data, FreSpeD identifies the correct brain region as the focal point of seizure, the time of seizure onset and the very subtle changes in cross-coherence immediately preceding seizure onset.

The goal of the second project to track changes in spatial boundaries (or more generally spatial sets or clusters) as the seizure process unfolds. A pair of channels (or a pair of sets of channels) are merged into one cluster if they exhibit synchronicity as measured by, for example, similarities in their spectra or by the strength of their coherence. We will highlight some open problems including developing a model for the evolutionary clustering of non-stationary time series.

The first project is in collaboration with Anna Louise Schröder (London School of Economics); the second is with Carolina Euan (CIMAT, Mexico), Joaquin Ortega (CIMAT, Mexico) and Ying Sun (KAUST, Saudi Arabia).

Mon, Oct 12, '15
16:00 - 17:00
CRiSM Seminar - Dan Roy (University of Toronto)
A1.01

Dan Roy (University of Toronto)
Nonstandard complete class theorems

For finite parameter spaces under finite loss, there is a close link between optimal frequentist decision procedures and Bayesian procedures:

every Bayesian procedure derived from a prior with full support is admissible, and every admissible procedure is Bayes. This relationship breaks down as we move beyond finite parameter spaces. There is a long line of work relating admissible procedures to Bayesian ones in more general settings. Under some regularity conditions, admissible procedures can be shown to be the limit of Bayesian procedures. Under additional regularity, they are generalized Bayesian, i.e., they minimize the average loss with respect to an improper prior. In both these cases, one must venture beyond the strict confines of Bayesian analysis.

Using methods from mathematical logic and nonstandard analysis, we introduce the notion of a hyperfinite statistical decision problem defined on a hyperfinite probability space and study the class of nonstandard Bayesian decision procedures---namely, those whose average risk with respect to some prior is within an infinitesimal of the optimal Bayes risk. We show that if there is a suitable hyperfinite approximation to a standard statistical decision problem, then every admissible decision procedure is nonstandard Bayes, and so the nonstandard Bayesian procedures form a complete class. We give sufficient regularity conditions on standard statistical decision problems admitting hyperfinite approximations. Joint work with Haosui (Kevin) Duanmu.

Fri, Jun 26, '15
14:00 - 16:00
CRiSM Seminar - Thomas Hamelryck (University of Copenhagan), Anjali Mazumder (Warwick)
D1.07 (Complexity)

Thomas Hamelryck (Bioinformatics Center, University of Copenhagen)

Inference of protein structure and ensembles using Bayesian statistics and probability kinematics

The so-called protein folding problem is the loose designation for an amalgam of closely related, unsolved problems that include protein structure prediction, protein design and the simulation of the protein folding process. We adopt a unique Bayesian approach to modelling bio-molecular structure, based on graphical models, directional statistics and probability kinematics. Notably, we developed a generative probabilistic model of protein structure in full atomic detail. I will give an overview of how rigorous probabilistic models of something as complicated as a protein's atomic structure can be formulated, focusing on the use of graphical models and directional statistics to model angular degrees of freedom. I will also discuss the reference ratio method, which is needed to "glue" several probabilistic models of protein structure together in a consistent way. The reference ratio method is based on "probability kinematics", a little known method to perform Bayesian inference proposed by the philosopher Richard C. Jeffrey at the end of the fifties. Probability kinematics might find widespread application in statistics and machine learning as a way to formulate complex, high dimensional probabilistic models for multi-scale problems by combining several simpler models.


Anjali Mazumder (University of Warwick)

Probabilistic Graphical Models for planning and reasoning of scientific evidence in the courts

The use of probabilistic graphical models (PGMs) has gained prominence in the forensic science and legal literature when evaluating evidence under uncertainty. The graph-theoretic and modular nature of the PGMs provide a flexible and graphical representation of the inference problem, and propagation algorithms facilitate the calculation of laborious marginal and conditional probabilities of interest. In giving expert testimony regarding, for example, the source of a DNA sample, forensic scientists under much scrutiny, are often asked to justify their decision-making-process. Using information-theoretic concepts and a decision-theoretic framework, we define a value of evidence criterion as a general measure of informativeness for a forensic query and collection of evidence to determine which and how much evidence contributes to the reduction of uncertainty. In this talk, we demonstrate how this approach can be used for a variety of planning problems and the utility of PGMs for scientific and legal reasoning.

 

Fri, Jun 12, '15
14:00 - 16:00
CRiSM Seminar - Sara van der Geer (Zurich), Daniel Simpson (Warwick)
D1.07 (Complexity)

Daniel Simpson (University of Warwick)

Penalising model component complexity: A principled practical approach to constructing priors

Setting prior distributions on model parameters is the act of characterising the nature of our uncertainty and has proven a critical issue in applied Bayesian statistics. Although the prior distribution should ideally encode the users’ uncertainty about the parameters, this level of knowledge transfer seems to be unattainable in practice and applied statisticians are forced to search for a “default” prior.

Despite the development of objective priors, which are only available explicitly for a small number of highly restricted model classes, the applied statistician has few practical guidelines to follow when choosing the priors. An easy way out of this dilemma is to re-use prior choices of others, with an appropriate reference.

In this talk, I will introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user- defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions.

Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations, like random effect models, spline smoothing, disease mapping, Cox proportional hazard models with time-varying frailty, spatial Gaussian fields and multivariate probit models. Further, we show how to control the overall variance arising from many model components in hierarchical models.

This joint work with Håvard Rue, Thiago G. Martins, Andrea Riebler, Geir-Arne Fuglstad (NTNU) and Sigrunn H. Sørbye (Univ. of Tromsø).

Sara van de Geer (ETH Zurich)

Norm-regularized Empirical Risk Minimization

Sara van de Geer Abstract

Fri, May 29, '15
14:00 - 16:00
CRiSM Seminar - Clifford Lam (LSE), Zoltan Szabo (UCL)
D1.07 (Complexity)

Zoltán Szabó, (UCL)

Regression on Probability Measures: A Simple and Consistent Algorithm

We address the distribution regression problem: we regress from probability measures to Hilbert-space valued outputs, where only samples are available from the input distributions. Many important statistical and machine learning problems can be phrased within this framework including point estimation tasks without analytical solution, or multi-instance learning. However, due to the two-stage sampled nature of the problem, the theoretical analysis becomes quite challenging: to the best of our knowledge the only existing method with performance guarantees requires density estimation (which often performs poorly in practise) and the distributions to be defined on a compact Euclidean domain. We present a simple, analytically tractable alternative to solve the distribution regression problem: we embed the distributions to a reproducing kernel Hilbert space and perform ridge regression from the embedded distributions to the outputs. We prove that this scheme is consistent under mild conditions (for distributions on separable topological domains endowed with kernels), and construct explicit finite sample bounds on the excess risk as a function of the sample numbers and the problem difficulty, which hold with high probability. Specifically, we establish the consistency of set kernels in regression, which was a 15-year-old-open question, and also present new kernels on embedded distributions. The practical efficiency of the studied technique is illustrated in supervised entropy learning and aerosol prediction using multispectral satellite images. [Joint work with Bharath Sriperumbudur, Barnabas Poczos and Arthur Gretton.]

 

Clifford Lam, (LSE)

Nonparametric Eigenvalue-Regularized Precision or COvariance Matrix Estimator for Low and High Frequency Data Analysis

We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size. With respect to the inverse Stein’s loss function, the inverse of our estimator is asymptotically the optimal precision matrix estimator. Asymptotic efficiency loss is defined through comparison with an ideal estimator, which assumed the knowledge of the true covariance matrix. We show that the asymptotic efficiency loss of NERCOME is almost surely 0 with a suitable split location of the data. We also show that all the aforementioned optimality holds for data with a factor structure. Our method avoids the need to first estimate any unknowns from a factor model, and directly gives the covariance or precision matrix estimator. Extension to estimating the integrated volatility matrix for high frequency data is presented as well. Real data analysis and simulation experiments on portfolio allocation are presented for both low and high frequency data.

Fri, May 15, '15
14:00 - 16:00
CRiSM Seminar - Carlos Carvalho (UT Austin), Andrea Riebler (Norwegian University of Science & Technology)
D1.07 (Complexity)

Carlos Carvalho, (The University of Texas)

Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective
Selecting a subset of variables for linear models remains an active area of research. This article reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

Andrea Riebler, (Norwegian University of Science and Technology)
Projecting cancer incidence and mortality: Bayesian age-period-cohort models ready for routine use
Projections of age-specific cancer data are of strong interest due to demographical changes, but also advances in medical diagnosis and treatment. Although Bayesian age-period-cohort (APC) models have been shown to be beneficial compared to simpler statistical models in this context, they are not yet used in routine practice. Reasons might be two-fold. First, Bayesian APC models have been criticised for producing too wide credible intervals. Second, there might be a lack of sound and at the same time easy-to-use software. Here, we address both concerns by introducing efficient MCMC-free software and showing that probabilistic forecasts obtained by the Bayesian APC model are well calibrated. We use hitherto annual lung cancer data for females in five different countries and omit the observations from the last 10 years. Consequently, we compare the yearly predictions with the actual observed data based on the absolute error and the continuous ranked probability score. Further, we assess calibration of one-step-ahead predictive distributions.

Fri, May 1, '15
14:00 - 16:00
CRiSM Seminar - Marcelo Pereyra (Bristol), Magnus Rattray (Manchester)
D1.07 (Complexity)
Marcelo Pereyra (Bristol)
Proximal Markov chain Monte Carlo: stochastic simulation meets convex optimisation
Convex optimisation and stochastic simulation are two powerful computational methodologies for performing statistical inference in high-dimensional inverse problems. It is widely acknowledged that these methodologies can complement each other very well, yet they are generally studied and used separately. This talk presents a new Langevin Markov chain Monte Carlo method that uses elements of convex analysis and proximal optimisation to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in modern high-dimensional statistics and data analysis. The method is based on a new first-order approximation for Langevin diffusions that uses Moreau-Yoshida approximations and proximity mappings to capture the log-concavity of the target density and construct Markov chains with favourable convergence properties. This approximation is closely related to Moreau-Yoshida regularisations for convex functions and uses proximity mappings instead of gradient mappings to approximate the continuous-time process. The proposed method complements existing Langevin algorithms in two ways. First, the method is shown to have very robust stability properties and to converge geometrically for many target densities for which other algorithms are not geometric, or only if the time step is sufficiently small. Second, the method can be applied to high-dimensional target densities that are not continuously differentiable, a class of distributions that is increasingly used in image processing and machine learning and that is beyond the scope of existing Langevin and Hamiltonian Monte Carlo algorithms. The proposed methodology is demonstrated on two challenging models related to image resolution enhancement and low-rank matrix estimation, which are not well addressed by existing MCMC methodology.


Magnus Rattray (Manchester)
Gaussian process modelling for omic time course data
We are developing methods based on Gaussian process inference for analysing data from high-throughput biological time course data. Applications range from classical statistical problems such as clustering and differential expression through to systems biology models of cellular processes such as transcription and it's regulation. Our focus is on developing tractable Bayesian methods which scale to genome-wide applications. I will describe our approach to a number of problems: (1) non-parametric clustering of replicated time course data; (2) inferring the full posterior of the perturbation time point from two-sample time course data; (3) inferring the pre-mRNA elongation rate from RNA polymerase ChIP-Seq time course data; (4) uncovering transcriptional delays by integrating pol-II and RNA time course data through a simple differential equation model.

Fri, Feb 20, '15
14:00 - 15:00
CRiSM Seminar - Marina Knight (York)
B1.01 (Maths)

Marina Knight (York)

Hurst exponent estimation for long-memory processes using wavelet lifting
Reliable estimation of long-range dependence parameters, such as the Hurst exponent, is a well-studied problem in the statistical literature. However, many time series observed in practice present missingness or are naturally irregularly sampled. In these settings, the current literature is sparse, with most approaches requiring heavy modifications in order to deal with the time irregularity. In this talk we present a technique for estimating the Hurst exponent of time series with long memory. The method is based on a flexible wavelet transform built by means of the lifting scheme, and is naturally suitable for series exhibiting time domain irregularity. We shall demonstrate the performance of this new method and illustrate the technique through time series applications in climatology.

Fri, Feb 6, '15
14:00 - 16:00
CRiSM Seminar - Gareth Peters (UCL), Leonhard Held (University of Zurich)
B1.01 (Maths)

Gareth Peters (UCL)
Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models
In this talk we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

Leonard Held (University of Zurich)
Adaptive prior weighting in generalized linear models
The prior distribution is a key ingredient in Bayesian inference. Prior information in generalized linear models may come from different sources and may or may not be in conflict with the observed data. Various methods have been proposed to quantify a potential prior-data conflict, such as Box's $p$-value. However, the literature is sparse on methodology what to do if the prior is not compatible with the observed data. To this end, we review and extend methods to adaptively weight the prior distribution. We relate empirical Bayes estimates of prior weight to Box's p-value and propose alternative fully Bayesian approaches. Prior weighting can be done for the joint prior distribution of the regression coefficients or - under prior independence - separately for each regression coefficient or for pre-specified blocks of regression coefficients. We outline how the proposed methodology can be implemented using integrated nested Laplace approximations (INLA) and illustrate the applicability with a logistic and a log-linear Poisson multiple regression model. This is joint work with Rafael Sauter.

Fri, Jan 23, '15
14:00 - 16:00
CRiSM Seminar - Rebecca Killick (Lancaster), Peter Green (Bristol)
B1.01 (Maths)

Rebecca Killick (Lancaster)
Forecasting locally stationary time series
Within many fields forecasting is an important statistical tool. Traditional statistical techniques often assume stationarity of the past in order to produce accurate forecasts. For data arising from the energy sector and others, this stationarity assumption is often violated but forecasts still need to be produced. This talk will highlight the potential issues when moving from forecasting stationary to nonstationary data and propose a new estimator, the local partial autocorrelation function, which will aid us in forecasting locally stationary data. We introduce the lpacf alongside associated theory and examples demonstrating its use as a modelling tool. Following this we illustrate the new estimator embedded within a forecasting method and show improved forecasting performance using this new technique.

Peter Green (Bristol)
Inference on decomposable graphs: priors and sampling
The structure in a multivariate distribution is largely captured by the conditional independence relationships that hold among the variables, often represented graphically, and inferring these from data is an important step in understanding a complex stochastic system. We would like to make simultaneous inference about the conditional independence graph and parameters of the model; this is known as joint structural and quantitative learning in the machine learning literature. The Bayesian paradigm allows a principled approach to this simultaneous inference task. There are tremendous computational and interpretational advantages in assuming the conditional independence graph is decomposable, and not too many disadvantages. I will present a new structural Markov property for decomposable graphs, show its consequences for prior modelling, and discuss a new MCMC algorithm for sampling graphs that enables Bayesian structural and quantitative learning on a much bigger scale than previously possible. This is joint work with Alun Thomas (Utah).

Tue, Dec 2, '14
14:00 - 16:00
CRiSM Seminar - David Draper (UC-Santa Cruz), Luis Nieto Barajas (ITAM - Instituto Tecnologico Autonomo de Mexico)
A1.01

Luis Nieto Barajas (ITAM - Instituto Tecnologico Autonomo de Mexico)
A Bayesian nonparametric approach for time series clustering
In this work we propose a model-based clustering method for time series. The model uses an almost surely discrete Bayesian nonparametric prior to induce clustering of the series. Specifically we propose a general Poisson-Dirichlet process mixture model, which includes the Dirichlet process mixture model as particular case. The model accounts for typical features present in a time series like trends, seasonal and temporal components. All or only part of these features can be used for clustering according to the user. Posterior inference is obtained via an easy to implement Markov chain Monte Carlo (MCMC) scheme. The best cluster is chosen according to a heterogeneity measure as well as the model selection criteria LPML (logarithm of the pseudo marginal likelihood). We illustrate our approach with a dataset of time series of shares prices in the Mexican stock exchange.

David Draper (University of California, Santa Cruz, USA, and Ebay Research Labs, San Jose, California, USA)
Why the bootstrap works; and when and why log scores are a good way to compare Bayesian models
In this talk I'll describe recent work on two unrelated topics:
(a) How the frequentist bootstrap may be understood as an approximate Bayesian non-parametric method, which explains why the bootstrap works and when it doesn't, and
(b) Why log scores are a good way to compare Bayesian models, and when they're better than Bayes factors at doing so.

Thu, Nov 27, '14
14:00 - 16:00
CRiSM Seminar - Daniel Williamson (Exeter) & David van Dyk (Imperial)
A1.01

David van Dyk (Imperial)
Statistical Learning Challenges in Astronomy and Solar Physics
In recent years, technological advances have dramatically increased the quality and quantity of data available to astronomers. Newly launched or soon-to-be launched space-based telescopes are tailored to data-collection challenges associated with specific scientific goals. These instruments provide massive new surveys resulting in new catalogs containing terabytes of data, high resolution spectrography and imaging across the electromagnetic spectrum, and incredibly detailed movies of dynamic and explosive processes in the solar atmosphere. The spectrum of new instruments is helping scientists make impressive strides in our understanding of the physical universe, but at the same time generating massive data-analytic and data-mining challenges for scientists who study the resulting data. In this talk I will introduce and discuss the statistical learning challenges inherent in data streams that are both massive and complex.

Daniel Williamson (Exeter)
Earth system models and probabilistic Bayesian calibration: a screw meets a hammer?
The design and analysis of computer experiments, now called “Uncertainty Quantification” or “UQ” has been an active area of statistical research for 25 years. One of the most high profile methodologies, that of calibrating a complex computer code using the Bayesian solution to the inverse problem as described by Kennedy and O’Hagan’s seminal paper in 2001, has become something of a default approach to tackling applications in UQ and has over 1200 citations. However, is this always wise? Though the method is well tested and arguably appropriate for many types of model, particularly those for which large amounts of data are readily available and in which the limitations of the underlying mathematical expressions and solvers are well understood, many models, such as those found in climate simulation, go far beyond those successfully studied in terms of non-linearity, run time, output size and complexity of the underlying mathematics. Have we really solved the calibration problem? To what extent is our “off the shelf approach” appropriate for the problems faced in fields such as Earth system modelling? In this talk we will discuss some of the known limitations of the Bayesian calibration framework (and some perhaps unknown) and we explore the extent to which the conditions in which calibration is known to fail are met in climate model problems. We will then present and argue for an alternative approach to the problem and apply it an ocean GCM known as NEMO.

Thu, Nov 13, '14
14:00 - 16:00
CRiSM Seminar - Michael Eichler (Maastricht) & Richard Huggins (Melbourne)
A1.01

Michael Eichler (Maastricht)
Causal Inference from Multivariate Time Series: Principles and Problems

In time series analysis, inference about cause-effect relationships among multiple time series is commonly based on the concept of Granger causality, which exploits temporal structure to achieve causal ordering of dependent variables. One major and well known problem in the application of Granger causality for the identification of causal relationships is the possible presence of latent variables that affect the measured components and thus lead to so-called spurious causalities. We present a new graphical approach for describing and analysing Granger-causal relationships in multivariate time series that are possibly affected by latent variables. It is based on mixed graphs in which directed edges represent direct influences among the variables while dashed edges---directed or undirected---indicate associations that are induced by latent variables. We show how such representations can be used for inductive causal learning from time series and discuss the underlying assumptions and their implications for causal learning. Finally we will discuss tetrad constraints in the time series context and how the can be exploited for causal inference.

Richard Huggins (Melbourne)
Semivarying Coefficient Models for Capture--recapture Data: Colony Size Estimation for the Little Penguin
To accommodate seasonal effects that change from year to year into models for the size of an open population we consider a time-varying coefficient model. We fit this model to a capture-recapture data set collected on the little penguin in south-eastern Australia over a 25 year period, using Jolly--Seber type estimators and nonparametric P-spline techniques. The time-varying coefficient model identified strong changes in the seasonal pattern across the years which we further examine using functional data analysis techniques.
(Joint work with Jakub Stoklosa of The University of New South Wales and Peter Dann from the Phillip Island Nature Parks.

Thu, Oct 30, '14
14:00 - 16:00
CRiSM Seminar - Pierre Jacob & Leonardo Bottolo
A1.01

Pierre Jacob
Estimation of the score vector and observed information matrix in intractable models
Ionides, King et al. (see Inference for nonlinear dynamical systems, PNAS 103) have introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to simulate the latent Markov model according its prior distribution. Their methodology bypasses the calculation of any derivative by expressing the score in the original model as an expectation under a modified model. Building upon this insightful work, we provide here a similar "derivative-free" estimator for the observed information matrix, expressed as a covariance matrix under a modified model. In principle the method is applicable for any latent variable model. We also discuss connections with Stein's method and proximal mappings.

Leonardo Bottolo
Mixture priors for subgroups classification
Technologies for the collection of genetic data, such as those based on RNA-Seq, are developing at a very fast rate. A crucial objective in these studies is gene clustering based on the similarity of their level of expression. A more important clustering task concerns samples themselves: this goes under the name of molecular profiling, and aims at identifying similarities across samples based on a few genes identified from the previous stage of the analysis.

In this talk we present a fully Bayesian hierarchical model for molecular profiling. A key ingredient of our approach is represented by the use of mixture distributions. First of all expression measurements are assumed to originate from a three-component mixture distribution, representing the underlying population classes (baseline, underexpression and overexpression) of samples relative to gene-expression. For each gene we assume a specific (random) probability of belonging to any of the three classes. Current Bayesian modelling assumes that the collection of gene-specific probabilities is exchangeable. Exchangeability assumption exhibits some drawbacks, the main one being its inability to capture heterogeneity in gene-behavior. This led us to model the gene-specific probabilities of under overexpression using a mixture of prior distributions with an unknown number of components: this represents the novelty of our approach which is meant to capture variation in gene behaviour and to identify clusters of genes in relation to their probability of under and overexpression.

The model is applied to gene expression levels from RNA-Seq analysis of left ventricular tissue derived from a cohort comprising 33 dilated cardiomyopathy patients with end-stage heart failure who underwent left ventricular assist device implant. Of these patients, 24 subsequently recovered their function whereas 9 did not. There is no obvious distinguishing features between them at the time the sample was taken. Molecular profiling is derived to predict recovery vs non-recovery patients. This is a joint work with Petros Dellaportas and Athanassios Petralias, Dept of Statistics, Athens University.

Thu, Oct 16, '14
14:00 - 16:00
CRiSM Seminar
A1.01

Karthik Bharath

Bayes robustness with Fisher-Rao metric.

A Riemannian-geometric framework is proposed to assess sensitivity of Bayesian procedures to modeling
assumptions based on the nonparametric Fisher–Rao metric; assessments include local and global robustness to perturbations of the likelihood and prior, and identification of influential observations. An important feature of the approach is in the unification of the perturbation and the inference via intrinsic analysis on the space of probability densities under the same Riemannian metric which leads to geometrically calibrated influence measures. Utility of the framework in interesting applications involving generalized mixed-effects and directional data models will be demonstrated.


Tony O’Hagan

"What can we do with a model that's wrong?"

People use models in all fields of science, technology, management, etc. These can range from highly complex mathematical models based on systems of differential equations to relatively simple empirical, statistical, models. This talk is about the uncertainty in the predictions made by models. One aspect of this has come to be called Uncertainty Quantification (UQ), and is concerned with deriving the uncertainty in model outputs induced by uncertainty in the inputs. But there is another component of uncertainty that is much more important: all models are wrong. This talk is about just how badly misled we can be if we forget this fact.

Wed, Oct 8, '14
16:00 - 17:00
CRiSM Seminar
MS.03

Christophe Ley - Universite Livre de Bruxelles

Stein's method, Information theory, and Bayesian statistics

In this talk, I will first describe a new general approach to the celebrated Stein method for asymptotic approximations and apply it to diverse approximation problems. Then I will show how Stein’s method can be successfully used in two a priori unrelated domains, namely information theory and Bayesian statistics. In the latter case, I will evaluate the influence of the choice of the prior on the posterior distribution at given sample size n. Based on joint work with Gesine Reinert (Oxford) and Yvik Swan (Liege).

Wed, Jul 16, '14
15:00 - 16:00
CRiSM Seminar - Adelchi Azzalini
A1.01

Adelchi Azzalini (University of Padova)

Clustering based on non-parametric density estimation: A proposal

Cluster analysis based on non-parametric density estimation represents an approach to the clustering problem whose roots date back several decades, but it is only in recent times that this approach could actually be developed. The talk presents one proposal within this approach which is among the few ones which have been brought up to the operational stage.

Thu, Jun 12, '14
15:00 - 16:00
CRiSM Seminar - Emmanuele Giorgi (Lancaster)

Emmanuele Giorgi (Lancaster)

Combining data from multiple spatially referenced prevalence surveys using generalized linear geostatistical models

Geostatistical methods are becoming more widely used in epidemiology to analyze spatial variation in disease prevalence. These methods are especially useful in resource-poor settings where disease registries are either non-existent or geographically incomplete, and data on prevalence must be obtained by survey sampling of the population of interest. In order to obtain good geographical coverage of the population, it is often necessary also to combine information from multiple prevalence surveys in order to estimate model parameters and for prevalence mapping.

However, simply fitting a single model to the combined data from multiple surveys is inadvisable without testing the implicit assumption that both the underlying process and its realization are common to all of the surveys. We have developed a multivariate generalized linear geostatistical model to combine data from multiple spatially referenced prevalence surveys so as to address each of two common sources of variation across surveys: variation in prevalence over time; variation in data-quality.

In the case of surveys that differ in quality, we assume that at least one of the surveys delivers unbiased gold-standard estimates of prevalence, whilst the others are potentially biased. For example, some surveys might use a random sampling design, the others opportunistic convenience samples. For parameter estimation and spatial predictions, we used Monte Carlo Maximum Likelihood methods.

We describe an application to malaria prevalence data from Chikhwawa District, Malawi. The data consist of two Malaria Indicator Surveys (MISs) and an Easy Access Group (EAG) study, conducted over the period 2010-2012. In the two MISs, the data were collected by random selection of households in an area of 50 villages within 400 square kilometers, whilst the EAG study enrolled a random selection of children attending the vaccination clinic in Chikhwawa District Hospital. The second sampling strategy is more economical, but the sampling bias inherent to such "convenience" samples needs to be taken into account.

 
14:00 - 15:00
CRiSM Seminar - Ben Graham (Warwick)
A1.01

Ben Graham (University of Warwick)

Handwriting, signatures, and convolutions

The 'signature', from the theory of differential equations driven by rough paths, provides a very efficient way of characterizing curves. From a machine learning perspective, the elements of the signature can be used as a set of features for consumption by a classification algorithm.

Using datasets of letters, digits, Indian characters and Chinese characters, we see that this improves the accuracy of online character recognition---that is the task of reading characters represented as a collection of pen strokes.

Thu, May 29, '14
15:00 - 16:00
CRiSM Seminar - Randal Douc
A1.01

Randal Douc (TELECOM SudParis)

Identifiability conditions for partially-observed Markov chains By R. Douc, F. Roueff and T. Sim

This paper deals with a parametrized family of partially-observed bivariate Markov chains. We establish that the limit of the normalized log-likelihood is maximized when the parameter belongs to the equivalence class of the true parameter, which is a key feature for obtaining consistency the Maximum Likelihood Estimators (MLE) in well-specified models. This result is obtained in a general framework including both fully dominated or partially dominated models, and thus applies to both Hidden Markov models or Observation-Driven times series. In contrast with previous approaches, the identifiability is addressed by relying on the unicity of the invariant distribution of the Markov chain associated to the complete data, regardless its rate of convergence to the equilibrium. We use this approach to obtain a set of easy-to-check conditions which imply the consistency of the MLE of a general observation driven time series.

 
14:00 - 15:00
CRiSM Seminar - Rajen Shah (Cambridge)
A1.01

Rajen Shah (Cambridge)

Random Intersection Trees for finding interactions in large, sparse datasets

Many large-scale datasets are characterised by a large number (possibly tens of thousands or millions) of sparse variables. Examples range from medical insurance data to text analysis. While estimating main effects in regression problems involving such data is now a reasonably well-studied problem, finding interactions between variables remains a serious computational challenge. As brute force searches through all possible interactions are infeasible, most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that potentially informative high-order interactions may be overlooked. Here, we propose an alternative approach for classification problems with binary predictor variables, called Random Intersection Trees. It works by starting with a maximal interaction that includes all variables, and then gradually removing variables if they fail to appear in randomly chosen observations of a class of interest. We show that with this method, under some weak assumptions, interactions can be found with high probability, and that the computational complexity of our procedure is much smaller than for a brute force search.

Thu, May 15, '14
15:00 - 16:00
CRiSM Seminar - David Leslie (Bristol)
A1.01

David Leslie (Bristol)
Applied abstract stochastic approximation

Stochastic approximation was introduced as a tool to find the zeroes of a function under only noisy observations of the function value. A classical statistical example is to find the zeroes of the score function when observations can only be processed sequentially. The method has since been developed and used mainly in the control theory, machine learning and economics literature to analyse iterative learning algorithms, but I contend that it is time for statistics to re-discover the power of stochastic approximation. I will introduce the main ideas of the method, and describe an extension; the parameter of interest is an element of a function space, and we wish to analyse its stochastic evolution through time. This extension allows the analysis of online nonparametric algorithms - we present an analysis of Newton's algorithm to estimate nonparametric mixing distributions. It also allows the investigation of learning in games with a continuous strategy set, where a mixed strategy is an arbitrary distribution on an interval.

(Joint work with Steven Perkins)

 
14:00 - 15:00
CRiSM Seminar - Mark Fiecas (Warwick)
A1.01

Mark Fiecas (Warwick)
Modeling the Evolution of Neurophysiological Signals

In recent years, research into analyzing brain signals has dramatically increased, and these rich data sets require more advanced statistical tools in order to perform proper statistical analyses. Consider an experiment where a stimulus is presented many times, and after each stimulus presentation (trial), time series data is collected. The time series data per trial exhibit nonstationary characteristics. Moreover, across trials the time series are non-identical because their spectral properties change over the course of the experiment. In this talk, we will look at a novel approach for analyzing nonidentical nonstationary time series data. We consider two sources of nonstationarity: 1) within each trial of the experiment and 2) across the trials, so that the spectral properties of the time series data are evolving over time within a trial, and are also evolving over the course of the experiment. We extend the locally stationary time series model to account for nonidentical data. We analyze a local field potential data set to study how the spectral properties of the local field potentials obtained from the nucleus accumbens and the hippocampus of a monkey evolve over the course of a learning association experiment.

Thu, May 1, '14
14:00 - 16:30
Oxford-Warwick Seminar: David Dunson (Duke) and Eric Moulines (Télécom ParisTech)
MS.03

David Dunson (Duke University)

Robust and scalable Bayes via the median posterior

Bayesian methods have great promise in big data sets, but this promise has not been fully realized due to the lack of scalable computational methods. Usual MCMC and SMC algorithms bog down as the size of the data and number of parameters increase. For massive data sets, it has become routine to rely on penalized optimization approaches implemented on distributed computing systems. The most popular scalable approximation algorithms rely on variational Bayes, which lacks theoretical guarantees and badly under-estimates posterior covariance. Another problem with Bayesian inference is the lack of robustness; data contamination and corruption is particularly common in large data applications and cannot easily be dealt with using traditional methods. We propose to solve both the robustness and the scalability problem using a new alternative to exact Bayesian inference we refer to as the median posterior. Data are divided into subsets and stored on different computers prior to analysis. For each subset, we obtain a stochastic approximation to the full data posterior, and run MCMC to generate samples from this approximation. The median posterior is defined as the geometric median of the subset-specific approximations, and can be rapidly approximated. We show several strong theoretical results for the median posterior, including general theorems on concentration rates and robustness. The methods are illustrated through simple examples, including Gaussian process regression with outliers.

Eric Moulines (Télécom ParisTech)

Proximal Metropolis adjusted Langevin algorithm for sampling sparse distribution over high-dimensional spaces

This talk introduces a new Markov Chain Monte Carlo method to sampling sparse distributions or to perform Bayesian model choices in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines (i) a Metropolis adjusted Langevin step to propose local moves associated with the differentiable part of the target density with (ii) a proximal step based on the non-differentiable part of the target density which provides sparse solutions such that small components are shrunk toward zero. Several implementations of the proximal step will be investigated adapted to different sparsity priors or allowing to perform variable selections, in high-dimensional settings. The performance of these new procedures are illustrated on both simulated and real data sets. Preliminary convergence results will also be presented.

Thu, Mar 27, '14
15:00 - 16:00
CRiSM Seminar - Professor Adrian Raftery (Washington)
A1.01

Professor Adrian Raftery (Washington)

Bayesian Reconstruction of Past Populations for Developing and Developed Countries

I will describe Bayesian population reconstruction, a new method for estimating past populations by age and sex, with fully probabilistic statements of uncertainty. It simultaneously estimates age-specific
population counts, vital rates and net migration from fragmentary data while formally accounting for measurement error. As inputs, it takes initial bias-corrected estimates of age-specific population counts, vital rates and net migration. The output is a joint posterior probability distribution which yields fully probabilistic interval estimates of past vital rates and population numbers by age and sex. It is designed for the kind of data commonly collected in demographic surveys and censuses and can be applied to countries with widely varying levels of data quality. This is joint work with Mark Wheldon, Patrick Gerland and Samuel Clark.

Thu, Mar 13, '14
14:00 - 16:00
CRiSM Seminar - Darren Wilkinson (Newcastle), Richard Everitt (Reading)
A1.01

Darren Wilkinson (Newcastle)
Stochastic Modelling of Genetic Interaction in Budding Yeast

Saccharomyces cerevisiae (often known as budding yeast, or brewers yeast) is a single-celled micro-organism that is easy to grow and genetically manipulate. As it has a cellular organisation that has much in common with the cells of humans, it is often used as a model organism for studying genetics. High-throughput robotic genetic technologies can be used to study the fitness of many thousands of genetic mutant strains of yeast, and the resulting data can be used to identify novel genetic interactions relevant to a target area of biology. The processed data consists of tens of thousands of growth curves with a complex hierarchical structure requiring sophisticated statistical modelling of genetic independence, genetic interaction (epistasis), and variation at multiple levels of the hierarchy. Starting from simple stochastic differential equation

(SDE) modelling of individual growth curves, a Bayesian hierarchical model can be built with variable selection indicators for inferring genetic interaction. The methods will be applied to data from experiments designed to highlight genetic interactions relevant to telomere biology.

Richard Everitt (Reading)

Inexact approximations for doubly and triply intractable problems

Markov random field models are used widely in computer science, statistical physics and spatial statistics and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to an intractable likelihood function. Several methods have been developed that permit exact, or close to exact, simulation from the posterior distribution. However, estimating the marginal likelihood and Bayes' factors for these models remains challenging in general. This talk will describe new methods for estimating Bayes' factors that use simulation to circumvent the evaluation of the intractable likelihood, and compare them to approximate Bayesian computation. We will also discuss more generally the idea of "inexact approximations".

Thu, Feb 13, '14
15:00 - 16:00
CRiSM Seminar - Vasileios Maroulas (Bath/Tennessee))
A1.01

Vasileios Maroulas (Bath/Tennessee)

Filtering, drift homotopy and target tracking

Abstract:
Target tracking is a problem of paramount importance arising in Biology, Defense, Ecology and other scientific fields. We attack to this problem by employing particle filtering. Particle filtering is an importance sampling method which may fail in several occasions, e.g. in high dimensional data. In this talk, we present a novel approach for improving particle filters suited to target tracking with a nonlinear observation model. The suggested approach is based on what I
will call drift homotopy for stochastic differential equations which describe the dynamics of the moving target. Based on drift homotopy, we design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particles closer to the observations while at the same time respecting the dynamics. The talk is based on joint works with Kai Kang and Panos Stinis.

 

 
14:00 - 15:00
CRiSM Seminar - Amanda Turner (Lancaster)
A1.01

Amanda Turner (Lancaster)

Small particle limits in a regularized Laplacian random growth model
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In 1998 Hastings and Levitov proposed a one-parameter family of models for planar random growth in which clusters are represented as compositions of conformal mappings. This family includes physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth. In the simplest case of the model (corresponding to the parameter alpha=0), James Norris and I showed how the Brownian web arises in the limit resulting from small particle size and rapid aggregation. In particular this implies that beyond a certain time, all newly aggregating particles share a single common ancestor. I shall show how small changes in alpha result in the emergence of branching structures within the model so that, beyond a certain time, the number of common ancestors is a random number whose distribution can be obtained. This is based on joint work with Fredrik Johansson Viklund (Columbia) and Alan Sola (Cambridge).

 

Thu, Jan 30, '14
14:00 - 16:00
CRiSM Seminar - Judith Rousseau (Paris Dauphine), Jean-Michel Marin (Université Montpellier)
A1.01

Jean-Michel Marin

Consistency of the Adaptive Multiple Importance Sampling (joint work with Pierre Pudlo and Mohammed Sedki

Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of a recycling procedure. However, the consistency of the AMIS estimator remains largely open. In this work, we prove the convergence of the AMIS, at a cost of a slight modification in the learning process. Numerical experiments exhibit that this modification might even improve the original scheme.

Judith Rousseau

Asymptotic properties of Empirical Bayes procedures – in parametric and non parametric models

 

In this work we investigate frequentist properties of Empirical Bayes procedures. Empirical Bayes procedures are very much used in practice in more or less formalized ways as it is common practice to replace some hyperparameter in the prior by some data dependent quantity. There are typically two ways of constructing these data dependent quantities : using some king of moment estimator or some quantity whose behaviour is well understood or using a maximum marginal likelihood estimator. In this work we first give some general results on how to determine posterior concentration rates under the former setting, which we apply in particular to two types of Dirichlet process mixtures. We then shall discuss more parametric models in the context of maximum marginal likelihood estimation. We will in particular explain why some pathological behaviour can be expected in this case.

Thu, Jan 16, '14
14:00 - 16:00
CRiSM Seminar - Chenlei Leng (Warwick), John Fox (Oxford & UCL/Royal Free Hospital)
A1.01

John Fox (Oxford & UCL/Royal Free Hospital)
Arguing logically about risks: strengths, limitations and a request for assistance
Abstract: The standard mathematical treatment of risk combines numerical measures of uncertainty (usually probabilistic) and loss (money and other natural estimators of utility). There are significant practical and theoretical problems with this interpretation. A particular concern is that the estimation of quantitative parameters is frequently problematic, particularly when dealing with one-off events such as political, economic or environmental disasters.
Consequently practical decision-making under risk often requires extensions to the standard treatment.
An intuitive approach to reasoning under uncertainty has recently become established in computer science and cognitive science based on argumentation theory. On this approach theories about an application domain (formalised in a non-classical first-order logic) are applied to propositional facts about specific situations, and arguments are constructed for and/or against claims about what might happen in those situations. Arguments can also attack or support other arguments. Collections of arguments can be aggregated to characterize the type or degree of risk, based on the grounds of the arguments. The grounds and form of an argument can also be used to explain the supporting evidence for competing claims and assess their relative credibility. This approach has led to a novel framework for developing versatile risk management systems and has been validated in a number of domains, including clinical medicine and toxicology (e.g. www.infermed.com; www.lhasa.com). Argumentation frameworks are also being used to support open discussion and debates about important issues (e.g. see debate on "planet under pressure" at http://debategraph.org/Stream.aspx?nid=145319&vt=bubble&dc=focus).

Despite the practical success of argumentation methods in risk management and other kinds of decision making the main theories ignore quantitative measurement of uncertainty, or they combine qualitative reasoning with quantitative uncertainty in ad hoc ways. After a brief introduction to argumentation theory I will demonstrate some medical applications and invite suggestions for ways of incorporating uncertainty probabilistically that are mathematically satisfactory.

Chenlei Leng (Warwick)

High dimensional influence measure


Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure. This is joint work with Junlong Zhao, Lexin Li, and Hansheng Wang.

A copy of the paper is downloadable from http://arxiv.org/abs/1311.6636.

Mon, Dec 9, '13
16:00 - 17:00
Seminar - Professor van Zanten
A1.01
Thu, Nov 28, '13
15:00 - 16:00
CRiSM Seminar - Christian Robert (Warwick)
A1.01

Selection of (ABC) summary statistics towards estimation and model choice

Abstract: The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions, which amount to the expectations of the summary statistics to asymptotically differ under both models, are then usable in ABC settings to determine which summary statistics are appropriate, via a standard and quick Monte Carlo validation. We also discuss new schemes to automatically select efficient summary statistics from a large collection of those.

(Joint work with J.-M. Marin, N. Pillai, P. Pudlo & J. Rousseau)

 
14:00 - 15:00
CRiSM Seminar - Oliver Ratmann (Imperial)
A1.01

Statistical modelling of summary values leads to accurate Approximate Bayesian Computations

Abstract: Approximate Bayesian Computations (ABC) are considered to be noisy. We present a statistical framework for accurate ABC parameter inference that rests on well-established results from indirect inference and decision theory. This framework guarantees that ABC estimates the mode of the true posterior density exactly and that the Kullback-Leibler divergence of the ABC approximation to the true posterior density is minimal, provided that verifiable conditions are met. Our approach requires appropriate statistical modelling of the distribution of "summary values" - data points on a summary level - from which the choice of summary statistics follows implicitly. This places elementary statistical modelling at the heart of ABC analyses, which we illustrate on several examples.

Thu, Oct 31, '13
15:00 - 16:00
CRiSM Seminar - Ben Francis (Liverpool)
A1.01

Ben Francis
Stochastic Control Methods to Individualise Drug Therapy by Incorporating Pharmacokinetic, Pharmacodynamic and Adverse Event Data
There are a number of methods available to aid determination of an individualised dosage regimen for a patient. However, often these methods are non-adaptive to the patient's requirements and do not allow for changing clinical targets throughout the course of therapy.

Research has been undertaken to include process noise in the Pharmacokinetic/Pharmacodynamic (PK/PD) response prediction to better simulate the patient response to the dose by allowing values sampled from the individual PK/PD parameter distributions to vary over time.

Further work explores different formulations of a cost function by considering probabilities from a Markov model.

Using the introduced methodology, the drug dose algorithm is shown to be adaptive to patient needs for imatinib and simvastatin therapy.

However, application of the drug dose algorithm in a wide range of clinical dosing decisions is possible.

 
14:00 - 15:00
CRiSM Seminar - Juhyun Park (Lancaster)
A1.01

Juhyun Park (Lancaster)
Functional average derivative regression
Abstract: Single index model is studied in the framework of regression estimation involving functional data. The model extends a linear model with an unknown link function and has the advantage of having low sensitivity to dimensional effects and flexibility and easiness of interpretation. However its usage in functional regression setting is still found to be limited, partly due to its complexity of fitting the model. In this work we develop a functional adaptation of the average derivative method that allows us to construct an explicit estimator for the functional single index.
Thanks to its explicit form of the estimator, implementation is made relatively simple and straightforward. Theoretical properties of the estimator of the index are studied based on asymptotic results on nonparametric functional derivatives estimation. In particular it is shown that the nonlinear regression component of the model can be estimated at the standard univariate rate, being therefore insensitive to the infinite dimensionality of the data.

Numerical examples are used to illustrate the method and to evaluate finite sample performance.

Thu, Oct 17, '13
14:00 - 16:00
CRiSM Seminar - François Caron (Oxford), Davide Pigoli (Warwick)
A1.01

François Caron (Oxford)
Bayesian nonparametric models for bipartite graphs

In this talk I will present a novel Bayesian nonparametric model for bipartite graphs, based on the theory of completely random measures. The model is able to handle a potentially infinite number of nodes and has appealing properties; in particular, it may exhibit a power-law behavior for some values of the parameters. I derive a posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation. Finally, the model is shown to provide a good fit to several large real-world bipartite social networks.

Davide Pigoli (Warwick)
Statistical methods for phonetic covariance operators in comparative linguistics

Comparative linguistics is concerned with the exploration of languages evolution. The traditional way of exploring relationships across languages consists of examining textual similarity. However, this neglects the phonetic characteristics of the languages. Here a novel approach is proposed to incorporate phonetic information, based on the comparison of frequency covariance structures in spoken languages. In particular, the aim is to explore the relationships among Romance languages and how they have developed from their common Latin root. The covariance operator being the statistical unit, a framework is illustrated for inference concerning the covariance operator of a functional random process. First, the problem of the definition of possible metrics for covariance operators is considered. In particular, an infinite dimensional analogue of the Procrustes reflection size and shape distance is developed. Then, distance-based inferential procedures are proposed for estimation and hypothesis testing. Finally, it is shown that the analysis of pairwise distances between phonetic covariance structures can provide insight into the relationships among Romance languages. Some languages also present features that are not completely expected from linguistics theory, indicatingnew directions for investigations.

 

Wed, Jul 10, '13
14:00 - 16:00
CRiSM Seminar - Prof Donald Martin
A1.01

Professor Donald Martin (North Carolina State University)

Computing probabilities for the discrete scan statistic through slack variables

The discrete scan statistic is used in many areas of applied probability and statistics to study local clumping of patterns.

Testing based on the statistic requires tail probabilities. Whereas the distribution has been studied extensively, most of the results are approximations, due to the difficulties associated with the computation. Results for exact tail probabilities for the statistic have been given for a binary sequence that is independent or first-order Markovian. We give an algorithm to obtain probabilities for the statistic over multi-state trials that are Markovian of a general order of dependence, and explore the algorithm’s usefulness.

Thu, Jun 27, '13
16:00 - 17:00
CRiSM Seminar - Nicolai Meinshausen
A1.01

Nicolai Meinshausen (University of Oxford)

Min-wise hashing for large-scale regression and classification.

We take a look at large-scale regression analysis in a "large p, large n" context for a linear regression or classification model.

In a high-dimensional "large p, small n" setting, we can typically only get good estimation if there exists a sparse regression vector that approximates the observations. No such assumptions are required for large-scale regression analysis where the number of observations n can (but does not have to) exceed the number of variables p. The main difficulty is that computing an OLS or ridge-type estimator is computationally infeasible for n and p in the millions and we need to find computationally efficient ways to approximate these solutions without increasing the prediction error by a large amount. Trying to find interactions amongst millions of variables seems to be an even more daunting task. We study a small variation of the b-bit minwse-hashing scheme (Li and Konig, 2011) for sparse datasets and show that the regression problem can be solved in a much lower-dimensional setting as long as the product of the number of non-zero elements in each observation and the l2-norm of a good approximation vector is small. We get finite-sample bounds on the prediction error. The min-wise hashing scheme is also shown to fit interaction models. Fitting interactions does not require an adjustment to the method used to approximate linear models, it just requires a higher-dimensional mapping.

Thu, Jun 13, '13
16:00 - 17:00
CRiSM Seminar - Piotr Fryzlewicz
A1.01

Piotr Fryzlewicz (London School of Economics)

Wild Binary Segmentation for multiple change-point detection

We propose a new technique, called Wild Binary Segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points, unlike standard Binary Segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to significant increase in computational complexity. WBS is also easy to code. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance. In addition, we provide a new proof of consistency of Binary Segmentation with improved rates of convergence, as well as a corresponding result for WBS.

Thu, Jun 6, '13
16:00 - 17:00
CRiSM Seminar - Ajay Jasra
A1.01

Ajay Jasra (National University of Singapore)

On the convergence of Adaptive sequential Monte Carlo Methods

In several implementations of Sequential Monte Carlo (SMC) methods, it is natural and important in terms of algorithmic efficiency, to exploit the information on the history of the particles to optimally tune their subsequent propagations. In the following talk we provide an asymptotic theory for a class of such adaptive SMC methods. Our theoretical framework developed here will cover for instance, under assumptions, the algorithms in Chopin (2002), Jasra et al (2011), Schafer & Chopin (2013). There are limited results about the theoretical underpinning of such adaptive methods: we will bridge this gap by providing a weak law of large numbers (WLLN) and a central limit theorem (CLT) for some of the algorithms. The latter seems to be the first result of its kind in the literature and provides a formal justification of algorithms that are used in many practical scenarios. This is a joint work with Alex Beskos (NUS/UCL).

Thu, May 30, '13
16:00 - 17:00
CRiSM Seminar - Tom Palmer
A1.01

Tom Palmer (Warwick Medical School)

Topics in instrumental variable estimation: structural mean models and bounds

One aim of epidemiological studies is to investigate the effect of a risk factor on a disease outcome. However, these studies are prone to unmeasured confounding and reverse causation. The use of genotypes as instrumental variables, known as Mendelian randomization studies, are one way to overcome this.

In this talk I describe some methods in instrumental variable estimation; structural mean models and nonparametric bounds for the average causal effect. Specifically, I describe how to estimate structural mean models using multiple instrumental variables in the generalized method of moments framework common in Econometrics. I describe the nonparametric bounds for the average causal effect of Balke and Pearl (JASA, 1997) which can be applied when each of the three variables; instrument, intermediate, and outcome are all binary.

I describe some methodological extensions to these bounds and their limitations.

To demonstrate the models I use a Mendelian randomization example investigating the effect of being overweight on the risk of hypertension in the Copenhagen General Population Study. I will also draw some comparisons with the application of instrumental variables to correct for noncompliance in randomized controlled trials.

Thu, May 23, '13
16:00 - 17:00
CRiSM Seminar - Ioanna Manolopoulou
A1.01

Ioanna Manolopoulou (University College London)

Bayesian observation modeling in presence-only data

The prevalence of presence-only samples eg. in ecology or criminology has led to a variety of statistical approaches. Aiming to predict ecological niches, species distribution models provide probability estimates of a binary response (presence/absence) in light of a set of environmental covariates. Similarly, statistical models to predict crime use propensity indicators from observable attributes inferred from incidental data. However, the associated challenges are confounded by non-uniform observation models; even in cases where observation is driven by seemingly irrelevant factors, these may distort estimates about the distribution of occurrences as a function of covariates due to unknown correlations. We present a Bayesian non-parametric approach to addressing sampling bias by carefully incorporating an observation model in a partially identifiable framework with selectively informative priors and linking it to the underlying process. Any available information about the role of various covariates in the observation process can then naturally enter the model. For example, in cases where sampling is driven by presumed likelihood of detecting an occurrence, the observation model becomes a proxy of the presence/absence model. We illustrate our methods on an example from species distribution modeling and a corporate accounting application.

Joint work with Richard Hahn from Chicago Booth.

Thu, May 2, '13
16:00 - 17:00
CRiSM Seminar - Jon Warren
A1.01

Dr Jon Warren (University of Warwick)

Random matrices, Stochastic Growth models and the KPZ equation.

I will base this talk on two pieces of joint work. One with Peter Windridge, the other with Neil O'Connell. Firstly I will show you how the distribution of a largest eigenvalue of certain random matrix ( in fact having a Wishart distribution) arises also in a simple stochastic growth model. In fact this growth model belongs to a large universality class, which includes mathematical models for interfaces as diverse as the edge of a burning piece of paper, or a colony of bacteria on a petri dish. The KPZ equation is a stochastic partial differential equation that also belongs to this universality class, and in the work with Neil we set out to construct an analogue, for the KPZ equation, for the second, third and so on largest eigenvalues of the random matrix.

Thu, Apr 25, '13
16:00 - 17:00
CRiSM Seminar - Heather Battey
A1.01

Heather Battey (University of Bristol)

Smooth projected density estimation

In this talk I will introduce a new class of estimators for multidimensional density estimation. The estimators are attractive in that they offer both flexibility and the possibility of incorporating structural constraints, whilst possessing a succinct representation that may be stored and evaluated easily. The latter property is of paramount importance when dealing with large datasets, which are now commonplace in many application areas. We show in a simulation study that the approach is universally unintimidated across a range of data generating mechanisms and often outperforms popular nonparametric estimators (including the kernel density estimator), even when structural constraints are not utilised. Moreover, its performance is shown to be somewhat robust to the choice of tuning parameters, which is an important practical advantage of our procedure.

Thu, Mar 14, '13
16:00 - 17:00
CRiSM Seminar - Kevin Korb (Monash)
A1.01

Kevin Korb (Monash)

An Overview of Bayesian Network Research at Monash

Recent research on and around Bayesian net (BN) technology at Monash has featured: fog forecasting (the Bureau of Meteorology); environmental management (Victorian gov); biosecurity (ACERA); finding better discretizations, using cost-based data and Bayesian scoring rules; data mining dynamic Bayesian networks; re-activating MML causal discovery of linear models. I'll discuss these and some other BN activities, briefly describe other research happening at Monash FIT, and the opportunities for collaboration.

Thu, Feb 28, '13
16:00 - 17:00
CRiSM Seminar - Andrew Golightly
A1.01

Andrew Golightly (Newcastle University)

Auxiliary particle MCMC schemes for partially observed Markov jump processes

We consider Bayesian inference for parameters governing Markov jump processes (MJPs) using discretely observed data that may be incomplete and subject to measurement error. We use a recently proposed particle MCMC scheme which jointly updates parameters of interest and the latent process and present a vanilla implementation based on a bootstrap filter before considering improvements based around an auxiliary particle filter. In particular, we focus on a linear noise approximation to the MJP to construct a pre-weighting scheme and couple this with a bridging mechanism. Finally, we embed this approach within a 'delayed acceptance' framework to allow further computational gains. The methods are illustrated with some examples arising in systems biology.

Thu, Feb 21, '13
16:00 - 17:00
CRiSM Seminar - Philip Dawid
A1.01

Philip Dawid (University of Cambridge

Theory and Applications of Proper Scoring Rules

We give an overview of the theory of proper scoring rules, and some recent applications.


A proper scoring rule encourages honest assessment of personal probabilities. It can also be used to define general entropy functions, discrepancy functions, M-estimators, etc., and to extend composite likelihood methods.

We have recently characterised those proper local scoring rules that can be computed without requiring the normalising constant of the density. This property is valuable for many purposes, including Bayesian model selection with improper priors.

 

Thu, Jan 31, '13
16:00 - 17:00
CRiSM Seminar - Catriona Queen
A1.01

Catriona Queen (The Open University)

A graphical dynamic approach to forecasting flows in road traffic networks

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This talk considers how cubic splines can be used to incorporate information from these extra variables to enhance flow forecasts. The talk also introduces a new type of chain graph model for forecasting traffic flows. The models are applied to the problem of forecasting multivariate road traffic flows at the intersection of three busy motorways near Manchester, UK.

Thu, Jan 24, '13
16:00 - 17:00
CRiSM Seminar - Evangelos Evangelou
A1.01

Evangelos Evangelou (University of Bath)

Spatial sampling design under cost constraints in the presence of sampling errors

A sampling design scheme for spatial models for the prediction of the underlying Gaussian random field will be presented. The optimality criterion is the maximisation of the information about the random field contained in the sample. The model discussed departs from the typical spatial model by assuming measurement error in the observations, varying from location to location, while interest lies in prediction without the error term. In this case multiple samples need to be taken from each sampling location in order to reduce the measurement error. To that end, a hybrid algorithm which combines simulated annealing nested within an exchange algorithm will be presented for obtaining the optimal sampling design. Consideration is made with regards to optimal sampling under budget constraints accounting for initialisation and sampling costs.

Joint work with Zhengyuan Zhu (Iowa State)

Thu, Jan 17, '13
16:00 - 17:00
CRiSM Seminar - Anastasia Papavasiliou (Warwick)
A1.01

Dr Anastasia Papavasiliou (University of Warwick)

Statistical Inference for differential equations driven by rough paths

Differential equations driven by rough paths (RDEs for short) generalize SDEs by allowing the equation to be driven by any type of noise and not just Brownian motion. As such, they are a very flexible modelling tool for randomly evolving dynamical systems. So far, however, they have been ignored by the statistics community, in my opinion for the two followin reasons: (i) the abstract theory of rough paths is still very young and under development, which makes it very hard to penetrate; (ii) there are no statistical tools available. In this talk, I will give an introduction to the theory and I will also discuss how to approach the problem of statistical inference given a discretely observed solution to an RDE.

Fri, Dec 14, '12
14:00 - 15:00
CRiSM Seminar - Bjarki Eldon
A1.01

Bjarki Eldon (Institut für Mathematik, TU Berlin)

Single, and multiple loci, large offspring number population models

For many organisms the usual Wright-Fisher and Moran low offspring number population models are reasonable approximations. For some marine organisms (at least), this may not be the case, and one may need to consider large offspring number models, in which individuals can give rise to very many offspring, or on the order of the population size. The coalescent processes derived from the two classes of population models are very different. Examples of single, and multiple loci, population models will be discusses, and the implications large offspring number models have for inference of, for example, natural selection.

Thu, Nov 29, '12
16:00 - 17:00
CRiSM Seminar - Nick Whiteley
A1.01

Nick Whiteley (University of Bristol)

Twisted Particle Filters

This talk reports on an investigation of alternative sampling laws for particle filtering algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. The focus is on the regime where the length of the data record tends to infinity.

Amongst a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from that of standard algorithms and yet the fluctuation properties of the estimates it provides are, in some ways, dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term "twisted" particle filters, and whose properties will be discussed.

Thu, Nov 22, '12
16:00 - 17:00
CRiSM Seminar - Piotr Zwiernik
A1.01

Piotr Zwiernik (TU Eindhoven)

Group invariance for Graphical Gaussian models

Graphical models are a popular way of modeling complicated dependencies. In the Gaussian case they have a particularly simple structure. Let G be an undirected graph with n nodes. Then the graphical Gaussian model is parametrized by the set K(G) of all concentration (symmetric, positive definite) matrices with zeros corresponding to non-edges of G. In this talk I describe the maximal subgroup of the general linear group that stabilizes K(G) in the natural action on symmetric matrices. This group gives the representation of graphical Gaussian models as composite transformation families, which has important consequences for the study of this model class. In particular I show how this links to the concept of robustness of covariance matrix estimators and more classical topics like hypotheses testing. (This is joint work with Jan Draisma and Sonja Kuhnt)

Thu, Nov 15, '12
16:00 - 17:00
CRiSM Seminar - Chris Sherlock
A1.01

Chris Sherlock (Lancaster University)

Inference for reaction networks using the Linear Noise Approximation

We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE), or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model, and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The Linear Noise Approximation (LNA) is a first order Taylor expansion of the approximating SDE about a deterministic solution. It can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how the LNA can be used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the method to the Google Flu Trends data for New Zealand, using an SEIR "community" model with separate compartments for North and South Islands.

Thu, Nov 8, '12
16:00 - 17:00
CRiSM Seminar - Robert G. Cowell
A1.01

 Robert G. Cowell (City University London)

A simple greedy algorithm for reconstructing pedigrees

I present a simple greedy-search algorithm for finding high likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but I believe that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not require age or sex information, but this information can be incorporated if desired. Prior information concerning pedigree structure is readily incorporated after the greedy-search is completed, on the high-likelihood pedigrees found.The algorithm is applied to human and non-human genetic data and in a simulation study.

Thu, Nov 1, '12
16:00 - 17:00
CRiSM Seminar - Patrick Wolfe
A1.01

Patrick Wolfe (UCL)

Modelling Network Data

Networks are fast becoming a primary object of interest in statistical data analysis, with important applications spanning the social, biological, and information sciences. A common aim across these fields is to test for and explain the presence of structure in network data. In this talk we show how characterizing the structural features of a network corresponds to estimating the parameters of various random network models, allowing us to obtain new results for likelihood-based inference and uncertainty quantification in this context. We discuss asymptotics for stochastic blockmodels with growing numbers of classes, the determination of confidence sets for network structure, and a more general point process modeling for network data taking the form of repeated interactions between senders and receivers, where we show consistency and asymptotic normality of partial-likelihood-based estimators related to the Cox proportional hazards model (arXiv:1201.5871, 1105.6245, 1011.4644, 1011.1703).

Thu, Oct 25, '12
16:00 - 17:00
CRiSM Seminar - Paul Jenkins
A1.01

Paul Jenkins (University of Warwick)

Sequential importance sampling and resampling in population genetic inference

Since 2008, the reduction in DNA sequencing costs has far outpaced Moore's law, giving rise to a wealth of data on sequence variation in contemporary populations. The patterns of variation we see are shaped both by biological processes such as mutation, recombination, and natural selection, and by demographic processes such as population expansion, contraction, and migration. In principle the nature of these processes can be inferred from the data, and one powerful approach is to use a stochastic model like Kingman's coalescent for the random genealogical relationships relating the sampled sequences. The problem then is to compute the likelihood under this model, which can be computationally very challenging. In this talk I will describe how we can make progress on this problem by using the Monte Carlo-based approaches of sequential importance sampling and resampling. I will discuss our approach to questions including the design of a suitable proposal distribution, and when and how to resample the particle-based approximation to the posterior distribution of genealogies.

Thu, Oct 18, '12
16:00 - 17:00
CRiSM Seminar - Ann Berrington
A1.01

Ann Berrington (Southampton University)

Title: Gender, turning points and boomerangs: longitudinal analyses of returning home in Britain

Thu, Oct 4, '12
16:00 - 17:00
CRiSM Seminar - Beatrijs Moerkerke
A1.01

Beatrijs Moerkerke (Ghent University, Belgium)

Estimation of controlled direct effects in the presence of exposure-induced confounding and latent variables

Estimation of the direct effect of an exposure on an outcome requires adjustment for confounders of the exposure-induced and mediator-outcome relationships. When some of these confounders are affected by the exposure, standard regression adjustment is prone to possibly severe bias. The use of inverse probability weighting has recently been suggested as a solution in the psychological literature. In this presentation, we present G-estimation as an alternative. We show that this estimation method can be easily embedded within the structural equation modeling framework and may in particular be used for estimating direct effects in the presence of latent variables. By avoiding inverse probability weighting, it accommodates the problem of unstable weights. We illustrate the approach both by simulations and by the analysis of an empirical study on the basis of which we explore the effect of age on negativity that is not mediated by mindfulness.

Mon, Jun 25, '12
12:00 - 13:15
CRiSM Seminar - Pat Carter (WSU, Biology)
A1.01

Pat Carter (WSU, Biology)
Evolution of Biological Shape: A Function-Valued Approach

Thu, May 31, '12
15:00 - 18:00
6th Oxford-Warwick Joint Seminar (at Warwick)
MS.02

15.00 - 16.00 Simon Tavaré (Cambridge)
Approximate Bayesian Computation for modeling DNA replication dynamics

16.30 - 17.30 Simon French (Warwick)
Aggregating expert judgement in major societal decisions

Thu, May 17, '12
16:00 - 17:00
CRiSM Seminar - Michael Sørensen
A1.01

Michael Sørensen (Copenhagen)
Martingale estimating functions for stochastic differential equations with jumps

Mon, May 14, '12
14:00 - 15:00
CRiSM Seminar - Anthony Lee (Warwick)
A1.01

Dr Anthony Lee (Warwick)

Thu, Mar 22, '12
16:00 - 17:00
CRiSM Seminar - Roberto Leon-Gonzalez
A1.01

Roberto Leon-Gonzalez, National Graduate Institute for Policy Studies, Tokyo

Endogeneity and Panel Data in Growth Regressions: A Bayesian Model Averaging Approach

In the empirical growth literature different modeling choices have led to substantially different qualitative results. Even on the basis of similar datasets, such differences can arise because of different set of instruments, exogeneity restrictions or set of controlling regressors. In this paper we develop a Bayesian Model Averaging (BMA) technique to deal with the large number of modeling choices that typically arise in the empirical growth literature. In particular, we present a general framework that not only allows for cross-section regressions with instrumental variables, but also for the commonly used dynamic panel data model with endogenous or predetermined regressors. We apply our technique to the long and inconclusive literature on the effect of international aid on GDP growth. We do not find evidence to support that international aid has an impact on GDP,
or that this impact is positive when conditioning on good macroeconomic policies. Instead we find strong evidence that macroeconomic policies, such as controlled inflation, are important
for GDP growth in developing countries.

Wed, Mar 14, '12
17:00 - 18:00
CRiSM Seminar - Heather Battey
A1.01

Heather Battey (University of Bristol)

Further details to follow

 
16:00 - 17:00
CRiSM Seminar - Heather Battey
A1.01

Heather Battey (University of Bristol)

Thu, Mar 1, '12
16:00 - 17:00
CRiSM Seminar - Graham Wood
A1.01

Graham Wood (Macquarie University and Warwick Systems Biology)

Normalization of ratio data

Quantitative mass spectrometry techniques are commonly used for comparative proteomic analysis in order to provide relative quantitation between samples. For example, in attempting to find the proteins expressed in ovarian cancer, the quantities of a given protein are assessed by mass spectrometry in separate samples of both cancerous and healthy cells. To account for the variable “loading” (the total volumes of samples) from one sample to the other, a normalization procedure is required. A common approach to normalization is to use internal standards, proteins that are assumed to display only minimal changes in abundance between the samples under comparison. A normalization procedure then allows adjustment of the data, so enabling true relative quantities to be reported.

Normalization is determined by centring the symmetrized ratio (say, cancerous over healthy) internal standards data. This presentation makes two contributions to an understanding of ratio normalization. First, the customary centring of logarithmically transformed ratios (frequently used, for example, in microarray analyses) is shown to attend not only to centring but also to minimisation of the spread of the symmetrized data. Second, the normalization problem is set in a larger context, allowing normalization to be achieved based on a symmetrization which carries the ratios to approximate normality, so increasing the power with which under or over-expressed proteins can be detected. Both simulated and real data will be used to illustrate the new method.

 
15:00 - 15:30
CRiSM Seminar - Stephen Connor
C1.06

Stephen Connor (University of York)

State-dependent Foster-Lyapunov criteria

Foster-Lyapunov drift criteria are a useful way of proving results about the speed of convergence of Markov chains. Most of these criteria involve examining the change in expected value of some function of the chain over one time step. However, in some situations it is more convenient to look at the change in expectation over a longer time period, which perhaps varies with the current state of the chain.

This talk will review some joint work with Gersende Fort (CNRS-TELECOM ParisTech), looking at when such state-dependent drift conditions hold and (perhaps more interestingly) what can be inferred from them. (Sadly I can't promise many pictures on this occasion, but I do promise not to show any proofs!)

Thu, Feb 16, '12
16:00 - 17:00
CRiSM Seminar - Yee Whye Teh
A1.01

Yee Whye Teh (Gatsby Computational Neuroscience Unit, UCL)

A Bayesian nonparametric model for genetic variations based on fragmentation-coagulation processes

Hudson's coalescent with recombination (aka ancestral recombination
graph (ARG)) is a well accepted model of genetic variation in
populations. With growing amounts of population genetics data, demand
for probabilistic models to analyse such data is strong, and the ARG
is a very natural candidate. Unfortunately posterior inference in the
ARG is intractable, and a number of approximations and alternatives
have been proposed. A popular class of alternatives are based on
hidden Markov models (HMMs), which can be understood as approximating
the tree-structured genealogies at each point of the chromosome with a
partition of the observed haplotypes. However due to the way HMMs
parametrize partitions using latent states, they suffer from
significant label-switching issues affecting the quality of posterior
inferences.

We propose a novel Bayesian nonparametric model for genetic variations
based on Markov processes over partitions called
fragmentation-coagulation processes. In addition to some interesting
properties, our model does not suffer from the label-switching issues
of HMMs. We derive an efficient Gibbs sampler for the model and report
results on genotype imputation.

Joint work with Charles Blundell and Lloyd Elliott

Thu, Feb 2, '12
16:00 - 17:00
CRiSM Seminar - Theodor Stewart
A1.01

Theodor Stewart (University of Cape Town)

Principles and Practice of Multicriteria Decision Analysis

The role of multicriteria decision analysis (MCDA) in the broader context of decision science will be discussed. We will review the problem structuring needs of MCDA, and caution against over-simplistic approaches. Different schools of thinking in MCDA, primarily for deterministic problems, will be introduced, to demonstrate that even such problems include many complexities and pitfalls. The practicalities will be illustrated by means of value function methods (and perhaps goal programming if time permits). We will conclude with consideration of the impact of uncertainty on MCDA and the role of scenario planning in this regard.

Mon, Jan 16, '12
12:00 - 13:00
CRiSM Seminar - Shinto Eguchi (Institute of Statistical Mathematics, Japan)
C1.06

Shinto Eguchi (Institute of Statistical Mathematics, Japan)

Maximization of a generalized t-statistic for linear discrimination in the two group classification problem

We discuss a statistical method for the classification problem with two groups labelled 0 and 1. We envisage a situation in which the conditional distribution given label 0 is well specified by a normal distribution, but the conditional distribution given label 1 is not well modelled by any specific distribution. Typically in a case-control study the distribution in the control group can be assumed to be normal, however the distribution in the case group may depart from normality. In this situation the maximum t-statistic for linear discrimination, or equivalently Fisher's linear discriminant function, may not be optiimal. We propose a class of generalized t-statistics and study asymptotic consistency and normality. The optimal generalized t-statistic in the sense of asymptotic variance is derived in a semi-parametric manner, and its statistical performance is confirmed in several numerical experiments.

Thu, Dec 1, '11
16:00 - 17:00
CRiSM Seminar - Mark Strong
A1.01

Mark Strong (University of Sheffield)

Managing Structural Uncertainty in Health Economic Decision Models

It was George Box who famously wrote ‘Essentially, all models are wrong’. Given our limited understanding of the highly complex world in which we live this statement seems entirely reasonable. Why then, in the context of health economic decision modelling, do we often act as if our models are right even if we know that they are wrong?

Imagine we have built a deterministic mathematical model to predict the costs and health effects of a new treatment, in comparison with an existing treatment. The model will be used by NICE to inform the decision as to whether to recommend the new treatment for use in the NHS.

The inputs to the model are uncertain, and we quantify the effect of this input uncertainty on the model output using Monte Carlo methods. We may even quantify the value of obtaining more information. We present our results to NICE as a fait accompli.

But, if we believe George Box then surely we should consider that our model output, our uncertainty analysis, and our estimates of the value of information are all ‘wrong’ because they are generated by a model that is ‘wrong’! The challenge is to quantify how wrong, and then determine the value of improving the model.

This seminar will explore the problem of structural uncertainty in health economic decision models, along with some suggested approaches to managing this uncertainty.

Thu, Nov 17, '11
16:00 - 17:00
CRiSM Seminar - Nick Chater (Warwick Business School)
A1.01
Nick Chater (Warwick Business School)
Is the brain a Bayesian?

Almost all interesting problems that the brain solves involve probabilities inference; and the brain is clearly astonishingly effective at solving such problems. A substantial movement in cognitive science, neuroscience and artificial intelligence has suggested that the brain may, to some approximation, be a Bayesian. This talk considers in what sense, if any, this might be true; and asks how it might be that a Bayesian brain might, nonetheless, so poor at explicit probabilistic reasoning.

Thu, Nov 3, '11
16:00 - 17:00
CRiSM Seminar - Dave Woods (Southampton)
A1.01

Dave Woods (University of Southampton)

Design of experiments for Generalised Linear (Mixed) Models

Generalised Linear and Generalised Linear Mixed Models (GLMs and GLMMs) may be used to describe data from a range of experiments in science, technology and industry. Example experiments with binary data come from areas such as crystallography, food science and aeronautical engineering. If the experiment is performed in blocks, eg subjects in a clinical trial or batches in manufacturing, a mixed model with random block effects allows the estimation of either subject-specific or population averaged treatment effects and induces an intra-block correlation structure for the response.

Finding optimal or efficient designs for GLMs and variants is complicated by the dependence of design performance on the values of the unknown model parameters. We describe methods for finding (pseudo) Bayesian designs that average a function of the information matrix across a prior distribution, and assess the resulting designs using simulation. The methods can also be extended to account for uncertainty in the linear predictor and link function, or to find designs for models with nonlinear predictors.

For GLMMs, the search for designs is complicated by the fact that the information matrix is not available in closed form. We make use of analytic and computational approximations, and also an alternative marginal model and generalised estimation equations.

 
15:00 - 15:45
CRiSM Seminar - Scott Schmidler (Duke University)
MS.01

Scott Schmidler (Duke University)

Bayesian Shape Matching for Protein Structure Alignment and Phylogeny

Understanding protein structure and function remains one of the great post-genome challenges of biology and molecular medicine. The 3D structure of a protein provides fundamental insights into its
biological function, mechanism, and interactions, and plays a key role in drug design. We have developed a Bayesian approach to modeling protein structure families, using methods adapted from the statistical
theory of shape. Our approach provides natural solutions to a variety of problems in the field, including pairwise and multiple alignment for the study of conservation and variability, algorithms for flexible
matching, and the impact of alignment uncertainty on phylogenetic tree reconstruction. Our recent efforts focus on extension to full evolutionary stochastic process models, which significantly improve upon
sequence-based phylogeny when divergence times are large.

Thu, Oct 20, '11
13:00 - 14:00
Joint CRiSM-Systems Biology Seminar
MOAC Seminar Room, Coventry House
Chris Brien (University of South Australia)
Robust Microarray Experiments by Design: A Multiphase Framework
This seminar will outline a statistical approach to the design of microarray experiments, taking account of all the experimental phases involved from initial sample collection to assessment of gene expression. The approach being developed is also highly relevant for other high-throughput technologies. This seminar should be of interest to all those working with experiments using microarray and other high-throughput technologies, as well as to statisticians.
Mon, Oct 17, '11
13:00 - 14:00
CRiSM Seminar - Atanu Biswas (Indian Statistical Institute)
B1.01

Atanu Biswas (Indian Statistical Institute)

Comparison of treatments and data-dependent allocation for circular data from a cataract surgery

Circular data is a natural outcome in many biomedical studies, e.g. some measurements in ophthalmologic studies, degrees of rotation of hand or waist, etc. With reference to a real data set on astigmatism induced in two types of cataract surgeries we carry out some two-sample testing problems including the Behren-Fisher type of test in the circular set up. Response-adaptive designs are used in phase III clinical trials to allocate a larger proportion of patients to the better treatment. There is no available work on response-adaptive designs for circular data. Here we provide some response-adaptive designs where the responses are of circular nature, first an ad-hoc allocation design, and then an optimal design. Detailed simulation study and the analysis of the data set, including resigning the cataract surgery data, are carried out.

Joint work with Somak Dutta (University of Chicago), Arnab Kumar Laha (Indian Institute of Management, Ahmedabad), Partho Bakshi (Disha Eye Hospitals, Barrackpore, India).

Thu, Oct 6, '11
16:00 - 18:00
CRiSM Seminar - Marek Kimmel (Rice University, Houston)
A1.01

Marek Kimmel, Rice University, Houston

Modeling the mortality reduction due to computed tomography screening for lung cancer

The efficacy of computed tomography (CT) screening for lung cancer remains controversial despite the fact that encouraging results from the National Lung Screening Trial are now available. In this study, the authors used data from a single-arm CT screening trial to estimate the mortality reduction using a modeling-based approach to construct a control comparison arm.

Fri, Jul 8, '11
11:00 - 12:30
Prof. Hernando Ombao - CRiSM Seminar
A1.01

Hernando Ombao

Analysis of non-stationary time series

Thu, Jul 7, '11
11:00 - 12:30
Prof. Hernando Ombao - CRiSM Seminar
A1.01

Hernando Ombao

Special topics on spectral analysis: principal components analysis, clustering and discrimination

 

Wed, Jul 6, '11
14:00 - 16:30
Prof. Hernando Ombao - CRiSM Seminar
A1.01

Hernando Ombao

Intro to spectral analysis and coherence

 

Thu, Jun 2, '11
16:00 - 17:00
CRiSM Seminar - Evsey Morozov
A1.01

Evsey Morozov (Karelian Research Centre, Russia)

Regenerative queues: stability analysis and simulation

We present a general approach to stability of regenerative queueing systems, which is based on the properties of the embedded renewal process of regenerations. Such a process obeys a useful characterization of the limiting remaining renewal time allowing in many cases to establish minimal stability conditions by a two-step procedure. At first step, a negative drift condition is used to prove that the basic process does not go to infinity (in probability), and at the second step, the finiteness of the mean regeneration period is proved. This approach has lead to the effective stability analysis of some models describing, in particular, such modern telecommunication systems as retrial queues and queues with optical buffers.

Moreover, we discuss regenerative simulation method including both classical and non-classical (extended) regeneration allowing a dependence between regeneration cycles.

Thu, May 26, '11
16:00 - 17:00
CRiSM Seminar - Postponed due to illness

 

Mon, May 23, '11
16:00 - 17:30
CRiSM PhD Talks
MS.03

Chris Nam (Warwick)
Quantifying the Uncertainty in Change Points in Time Series

Bryony Hill (Warwick)
A Gradient Field Approach to Modelling Fibre-Generated Spatial Point Processes

Ashley Ford (Warwick)
Indian Buffet Epidemics - A non-parametric Bayesian Approach to Modelling Heterogeneity

Thu, May 19, '11
16:00 - 17:00
CRiSM Seminar - Sumeetpal Singh
A1.01

Sumeetpal Singh (Cambridge)

Computing the filter derivative using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a SMC algorithm to compute the derivative of the optimal filter in a Hidden Markov Model (HMM) and study its stability both theoretically and with numerical examples. Applications include calibrating the HMM from observed data in an online manner.

(Joint work with P. Del Moral and A. Doucet)

Thu, May 12, '11
16:00 - 17:00
CRiSM Seminar - Alexander Gorban
A1.01

Alexander Gorban (Leicester)

Geometry of Data Sets

Plan
1. The problem
2. Approximation of multidimensional data by low-dimensional objects
2.1. Principal manifolds and elastic maps
2.2. Principal graphs and topological grammars
2.3. Three types of complexity: geometrical, topological and algorithmic
3. Self-simplification of essentially high-dimensional sets
4. Terra Incognita between low-dimensional sets and self-simplified high-dimensional ones.
5. Conclusion and open problems

Thu, Apr 28, '11
16:00 - 17:00
CRiSM Seminar - Sofia Massa
A1.01

Dr Sofia Massa (Oxford)

Combining information from graphical Gaussian models

In some recent applications, the interest is in combining information about relationships between variables from independent studies performed under partially comparable circumstances. One possible way of formalising this problem is to consider combination of families of distribution respecting conditional independence constraints with respect to a graph G, i.e., graphical models. In this talk I will introduce some motivating examples of the research question and I will present some relevant types of combinations and associated properties, in particular the relation between the properties of the combination and the structure of the graphs. Finally I will discuss some issues related to the estimation of the parameters of the combination.

Thu, Mar 24, '11
16:00 - 17:00
CRiSM Seminar - Carlos Navarette
A1.01

Carlos Navarette (Universidad de La Serena)

Similarity analysis in Bayesian random partition models

This work proposes a method to assess the influence of individual observations in the clustering generated by any process that involves random partitions. It is called Similarity Analysis. It basically consists of decomposing the estimated similarity matrix into an intrinsic and an extrinsic part, coupled with a new approach for representing and interpreting partitions. Individual influence is associated with the particular ordering induced by individual covariates, which in turn provides an interpretation of the underlying clustering mechanism. Some applications in the context of Species Sampling Mixture Models will be presented, including Bayesian density estimation, dependent linear regression models and logistic regression for bivariate response. Additionally, an application to time series modelling based on time-dependent Dirichlet processes will be outlined.

Thu, Feb 24, '11
16:00 - 17:00
CRiSM Seminar - Iain Murray
A1.01

Iain Murray (University of Edinburgh)

Sampling latent Gaussian models and hierarchical modelling

Sometimes hyperparameters of hierarchical probabilistic models are not well-specified enough to be optimized. In some scientific applications inferring their posterior distribution is the objective of learning.

Using a simple example, I explain why Markov chain Monte Carlo (MCMC) simulation can be difficult, and offer a solution for latent Gaussian models.

Thu, Feb 17, '11
16:00 - 17:00
CRiSM Seminar - Wicher Bergsma
A1.01

Wicher Bergsma (LSE) Marcel Croon, Jacques Hagenaars

Marginal Models for Dependent, Clustered, and Longitudinal Categorical Data

  

In the social, behavioural, educational, economic, and biomedical sciences, data are often collected in ways that introduce dependencies in the observations to be compared. For example, the same respondents are interviewed at several occasions, several members of networks or groups are interviewed within the same survey, or, within families, both children and parents are investigated. Statistical methods that take the dependencies in the data into account must then be used, e.g., when observations at time one and time two are compared in longitudinal studies. At present, researchers almost automatically turn to multi-level models or to GEE estimation to deal with these dependencies.

Despite the enormous potential and applicability of these recent developments, they require restrictive assumptions on the nature of the dependencies in the data. The marginal models of this talk provide another way of dealing with these dependencies, without the need for such assumptions, and can be used to answer research questions directly at the intended marginal level. The maximum likelihood method, with its attractive statistical properties, is used for fitting the models.

This talk is based on a recent book by the authors in the Springer series Statistics for the Social Sciences, see www.cmm.st.

 

Thu, Feb 3, '11
16:00 - 17:00
CRiSM Seminar - Simon Spencer
A1.01

Simon Spencer (Warwick)

Outbreak detection for campylobacteriosis in New Zealand

Identifying potential outbreaks of campylobacteriosis from a background of sporadic cases is made more difficult by the large spatial and temporal variation in incidence. One possible approach involves using Bayesian hierarchical models to simultaneously estimate spatial, temporal and spatio-temporal components of the risk of infection. By assuming that outbreaks are characterized by spatially localised periods of increased incidence, it becomes possible to calculate an outbreak probability for each potential disease cluster. The model correctly identifies known outbreaks in data from New Zealand for the period 2001 to 2007. Studies using simulated data have shown that by including epidemiological information in the model construction, this approach can outperform an established method.

Thu, Jan 27, '11
16:00 - 17:00
CRiSM Seminar - Alberto Sorrentino

Alberto Sorrentino (Warwick)

Bayesian filtering for estimation of brain activity in magnetoencephalography

Magnetoencephalography (MEG) is a sophisticated technique measuring the tiny magnetic fields produced by the brain activity. Relative to other functional neuroimaging techniques MEG recordings feature an outstanding temporal sampling resolution, in principle allowing for a study of the neural dynamics on a millisecond-by-millisecond time scale, but the spatial localization of neural currents from MEG data turns out to be an ill-posed inverse problem, i.e. a problem which has infinitely many solutions. To mitigate ill-posedness, a variety of parametric models of the neural currents are proposed in the burgeoning neuroimaging literature. In particular, under suitable approximations the problem of estimating brain activity from MEG data can be re-phrased as a Bayesian filtering problem with an unknown and time-varying number of sources.

In this talk I will first illustrate a statistical model of source localisation for MEG data which builds directly on the well-established Physics of the electro-magnetic brain field. The focus of the talk will then be to describe the application of a recently developed class of sequential Monte Carlo methods (particle filters) for estimation of the model parameters using empirical MEG data.

Thu, Jan 20, '11
16:00 - 17:00
CRiSM Seminar - Jouni Kuha

Jouni Kuha (London School of Economics)

Sample group means in multilevel models: Sampling error as measurement error

Research questions for models for clustered data often concern the effects of cluster-level averages of individual-level variables.  For example, data from a social survey might characterise neigborhoods in
terms of average income, ethnic composition etc. of people within each neighbourhood. Unless the true values of such averages are known from some other source, they are typically estimated by within-cluster
sample estimates, using data on the subjects in the observed data. This incurs a measurement error bias when these estimates are used as explanatory variables in subsequent modelling, even if the individual observations are measured without error. The measurement error variance can, however, be estimated from within-cluster variation, using knowledge of the sampling design within each cluster, and we can then apply relatively standard measurement error methods to adjust for the error. This talk considers such estimation for generalised linear mixed models, comparing common measurement error adjustments to naive analysis with no adjustment.

Thu, Jan 13, '11
16:00 - 17:00
CRiSM Seminar - Tilman Davies
A1.01

Tilman Davies (Massey University, NZ)

Refining Current Approaches to Spatial and Spatio-Temporal Modelling in Epidemiology

It is reasonable to expect both space and time to be important factors when investigating disease in human, animal and even plant populations. A common goal in many studies in geographical epidemiology, for example, is the idenification of disease risk 'hotspots', where spatial sub-regions that correspond to a statistically significant increase in the risk of infection are highlighted. More advanced problems involving not just space but space-time data, such as real-time disease surveillance, can be difficult to model due to complex correlation structures and computationally demanding operations. Decisions based on these kinds of analyses can range from the local, to national and even global levels. It is therefore important we continue to improve statistical methodology in this relatively young field, and ensure any theoretical benefits can flow through in practice.

This talk aims to give an overview of the PhD research currently underway in an effort to develop and implement refinements to spatial and spatio-temporal modelling. Of note include use of a spatially adaptive smoothing parameter for estimation of the kernel-smoothed relative-risk function, development of a novel, computationally inexpensive method for associated spatial tolerance contour calculation, release of an R package implementing these capabilities, and the scope for improvement to the current marginal minimum-contrast methods for parameter estimation in relevant stochastic models.

Thu, Dec 9, '10
16:00 - 17:00
CRiSM Seminar - Ayanendranath Basu
A1.01

Ayanendranath Basu (Indian Statistical Institute)

Contamination Envelopes for Statistical Distances with Applications to Power Breakdown 
 
Inference procedures based on density based distances are known for their high efficiency and strong robustness. Similarly, other distance based analogues of the likelihood ratio test combine some of the properties of this test with good robustness properties. In this work we will derive general contamination envelopes for the distances under data contamination which have immediate application in deriving the power breakdown bounds for parametric tests of hypothesis based on density based distances. Our results will generalize and improve the existing power breakdown bounds for parametric tests based on distances. The talk will focus on the theoretical and computational issues related to this problem.

Thu, Dec 2, '10
16:00 - 17:00
CRiSM Seminar - Matti Vihola
MS.01

Matti Vihola (University of Jyväskylä)

On the stability and convergence of adaptive MCMC 

Adaptive MCMC algorithms tune the proposal distribution of the Metropolis-Hastings Markov kernel continuously using the simulated history of the chain. There are many applications where AMCMC algorithms are empirically shown to improve over the traditional MCMC methods. Due to the non-Markovian nature of the adaptation, however, the analysis of these algorithms requires more care than the traditional methods.

Most results on adaptive MCMC in the literature are based on assumptions that require the adaptation process to be `stable' (in a certain sense).

Such stability can rarely be established unless the process is modified by introducing specific stabilisation structures. The most straightforward strategy is to constrain the adaptation within certain pre-defined limits.

Such limits may sometimes be difficult to choose in practice, and the algorithms are generally sensitive to these parameters. In the worst case, poor choices can render the algorithms useless.

This talk focuses on the recent stability and ergodicity results obtained for adaptive MCMC algorithms without such constraints. The key idea behind the results is that the ergodic averages can converge even if the Markov kernels gradually `lose' their ergodic properties. The new approach enables to show some sufficient conditions for stability and ergodicity for random walk Metropolis algorithms: the seminal Adaptive Metropolis algorithm and an algorithm adjusting the scale of the proposal distribution based on the observed acceptance probability.  The results assume only verifiable conditions on the target distribution and the functional.

Thu, Nov 25, '10
16:00 - 17:00
CRiSM Seminar - Andrew Grieve
A1.01

Andrew Grieve (King's College London)

Recent developments in Bayesian Adaptive design

Thu, Nov 18, '10
14:30 - 18:30
Joint Oxford-Warwick Seminar
Oxford: Tsuzuki Lecture Theatre, St Anne's College, Woodstock Road

2:30  Philip Dawid (University of Cambridge)

Local Proper Scoring Rules

A scoring rule S(x, Q) measures the quality of a quoted distribution Q for an uncertain quantity X in the light of the realised value x of X.  It is proper when it encourages honesty, i.e, when, if your uncertainty about X is represented by a distribution P, the choice Q = P minimises your expected loss. Traditionally, a scoring rule has been called local if it depends on Q only through q(x), the density of Q at x.  The only proper local scoring rule is then the log-score, -log q(x).  For the continuous case, we can weaken the definition of locality to allow dependence on a finite number m of derivatives of q at x.  A characterisation is given of such order-m local proper scoring rules, and their behaviour under transformations of the outcome space. In particular, any m-local scoring rule with m > 0 can be computed without knowledge of the normalising constant of the density. Parallel results for discrete spaces will be given.

3:30 - 4:00 Tea break

4:00  Christl Donnelly (Imperial College London)

Badger culling to control bovine TB: its potential role in a science-led policy

In 1997 the so-called Krebs Report recommended a randomized field trial be undertaken to evaluate the effectiveness of badger culling as a method of reducing bovine TB incidence in cattle herds.  The Randomised Badger Culling Trial was carried out in 30 100-sq-km areas. Along with related studies, it provided insights into several epidemiological aspects of the multi-species disease system.  The coalition government is currently seeking views on its proposal to include badger culling as a component of a science-led policy to control bovine TB.  

5:00 Reception to be held in Foyer A, Ruth Deech Building

Thu, Nov 11, '10
16:00 - 17:00
CRiSM Seminar - Richard Gill
A1.01

Richard Gill (Leiden University)

Murder by numbers

In March 2003, Dutch nurse Lucia de Berk was sentenced to life imprisonment by a court in The Hague for 5 murders and 2 murder attempts of patients in her care at a number of hospitals where she had worked in the Hague between 1996 and 2001.  The only hard evidence against her was a statistical analysis resulting in a p-value of 1 in 342 million which purported to show that it could not be chance that so many incidents and deaths occured on her ward while she was on duty. On appeal in 2003 the life sentence was confirmed, this time for 7 murders and 3 attempts. This time, no statistical evidence was used at all: all the deaths were proven to be unnatural and Lucia shown to have caused them using scientific medical evidence only. However, after growing media attention and pressure by concerned scientists, including many statisticians, new forensic investigations were made which made showed that the conviction was unsafe. After a new trial, Lucia was spectacularly and completely exhonerated in 2010. 

I'll discuss the statistical evidence and show how it became converted into incontrovertible medical-scientific proof in order to secure the second, and as far as the Dutch legal system was concerned, definitive conviction. I'll also show how statisticians were instrumental in convincing the legal establishment that Lucia should be given a completely new trial. The history of Lucia de Berk brought a number of deficiencies to light in the way in which scientific evidence is evaluated in criminal courts. Similar cases to that of Lucia occur regularly all over the world. The question of how that kind of data should be statistically analyzed is still problematic. I believe that there are also important lessens to be learnt by the medical world, however, the Dutch medical community, where most people still believe Lucia is a terrible serial killer, is resisting all attempts to uncover what really happened.

Thu, Nov 4, '10
16:00 - 17:00
CRiSM Seminar - Jianxin Pan
A1.01

Jianxin Pan (University of Manchester)

Joint modelling of mean and covariance structures for longitudinal data

When analysing longitudinal/correlated data, misspecification of covariance structures may lead to very inefficient estimators of parameters in the mean. In some circumstances, e.g., when missing data are present, it may result in biased estimators of the mean parameters. Hence, correct models for covariance structures play a very important role. Like the mean, covariance structures can be actually modelled using linear or nonlinear regression model techniques. A number of estimation methods were developed recently for modelling of mean and covariance structures, simultaneously. In this talk, I will review some methods on joint modelling of the mean and covariance structures for longitudinal data, including linear, non-linear regression models and semiparametric models. Real examples and simulation studies will be provided for illustration.

Thu, Oct 28, '10
16:00 - 17:00
CRiSM Seminar - Sofia Olhede
A1.01

Sofia Olhede (UCL)

Estimation of Nonstationary Time Series

A time series is usually, unless a specific parametric model is assumed, understood from its first and second moments. If the process is also stationary, e.g. its first and second moments are invariant to time translations, then estimation is a mature and well-developed field.

Unfortunately, most observed processes are not stationary, as they are the result of the observation of transient phenomena. Therefore in classical time series analysis a theory has also been developed for the analysis of such processes. There are a number of short-comings of existing and well-developed methods, in particular in how the processes are allowed to evolve in time. I will discuss how to relax existing assumptions and still be able to develop good inference methods from a single time course of observations.

Thu, Oct 21, '10
16:00 - 17:00
CRiSM Seminar - Richard Boys
A1.01

Richard Boys (Newcastle University)

Linking systems biology models to data: a stochastic kinetic model of p53 oscillations

This talk considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in this response, captured at the level of individual cells in a human cancer cell line. The primary goal of is to "calibrate" the model by finding parameters of the model (kinetic rate constants) that are most consistent with the experimental data. Significant amounts of prior information are available for the model parameters. It is therefore most natural to consider a Bayesian analysis of the problem, using sophisticated MCMC methods to overcome the formidable computational challenges.

Thu, Oct 14, '10
16:00 - 17:00
CRiSM Seminar - Ajay Jasra
A1.01

Ajay Jasra (Imperial College London)

The Time Machine: A Simulation Approach for Stochastic Trees 

One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling  and sequential Monte Carlo techniques. The approach proceeds by simulating, backward in time from observed data, to a most recent common ancestor.

However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this talk I propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface.  The bias investigated from a theoretical point of view. Also, extensive simulation results are given, which justify the loss of accuracy with significant savings in computational time. This is a joint work with Maria De Iorio and Marc Chadeau-Hyam.

Thu, Sep 23, '10
16:00 - 17:00
CRiSM Seminar - Tim Johnson
A1.01

Timothy D. Johnson (University of Michigan)

Predicting Treatment Efficacy via Quantitative MRI: A Bayesian Joint Model  Abstract
 
11:00 - 12:00
CRiSM Lectures
A1.01

Tim Johnson

Lecture 3: Simulation and Bayesian Methods
Thursday 23 Sept, 11-noon, A1.01

1. Spatial Birth and Death Process Algorithm and Alternatives

2. Fast Computation for Log-Gaussian Cox Processes

3. Bayesian Methods for
   (a) Independent Cluster Processes
   (b) Log-Gaussian Cox Processes
Tue, Sep 21, '10
11:00 - 12:00
CRiSM Lectures
A1.01

Tim Johnson

Lecture 2: Aggregative, Repulsive and Marked Point Processes
Tuesday 21 Sept, 11-noon, A1.01

1. Cluster Point Processes
   (a) Independent Cluster Process
   (b) Log-Gaussian Cox Process

2. Markov Point Processes
   (a) Hard-Core Process
   (b) Strauss Process

3. Marked Point Processes
Mon, Sep 20, '10
11:00 - 12:00
CRiSM Lectures
A1.01

Tim Johnson

Lecture 1: Introduction to Spatial Point Processes
Monday 20 Sept, 11-noon, A1.01

1. Introduction

2. Spatial Poisson Process

3. Spatial Cox Processes
Mon, Jul 26, '10
14:00 - 15:00
CRiSM Seminar - Andrew Gelman
A1.01

Andrew Gelman (Columbia University)

Nothing is Linear, Nothing is Additive: Bayesian Models for Interactions in Social Science

Tue, Jul 13, '10
14:00 - 15:00
CRiSM Seminar - Freedom Gumedze (University of Cape Town)
A1.01
Freedom Gumedze (University of Cape Town)
 
An alternative approach to outliers in meta-analysis
 
Meta-analysis involves the combining of estimates from independent studies on some treatment in order to get an estimate across studies. However, outliers often occur even under the random effects model. The presence of such outliers could alter the conclusions in a meta-analysis. This paper proposes a methodology that detects and accommodates outliers in a meta-analysis rather than remove them to achieve homogeneity. An outlier is taken as an observation (study result) with inflated random effect variance, with the status of the ith observation as an outlier indicated by the size of the associated shift in the variance. We use the likelihood ratio test statistic as an objective measure for determining whether the ith observation has inflated variance and is therefore an outlier. A parametric bootstrap procedure is proposed to obtain the sampling distribution for the likelihood ratio test and to account for multiple testing. We illustrate the methodology and its usefulness using three meta-analysis data sets from the Cochrane Collaboration.
Fri, Jun 25, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Jim Nolen (Duke)
Thu, Jun 24, '10
16:00 - 17:00
CRiSM Seminar - Sujit Sahu (Southampton)
A1.01

Sujit Sahu (Southampton)

High Resolution Bayesian Space-Time Modelling for Ozone Concentration Levels

Ground-level ozone is a pollutant that is a significant health risk, especially for children with asthma. It also damages crops, trees and other vegetation. It is a main ingredient of urban smog. To evaluate exposure to ozone levels, the  United States Environmental Protection Agency (USEPA) has developed a primary and a secondary air quality standard. To assess compliance to these standards, the USEPA collects ozone concentration data continuously from several networks of sparsely and irregularly spaced monitoring sites throughout the US. Data obtained from these sparse networks must be processed using spatial and spatio-temporal methods to check compliance to the ozone standards at an unmonitored site in the vast continental land  mass of the US. 

This talk will first discuss the two air quality standards for ozone levels and then will develop high resolution Bayesian space-time models which can be used to assess compliance. Predictive inference properties of several rival modelling strategies for both spatial interpolation and temporal forecasting will be compared and illustrated with simulation and real data examples. A number of large real life ozone concentration data sets observed over the eastern United States will also be used to illustrate the Bayesian space-time models. Several prediction maps from these models for the eastern US, published and used by the USEPA, will be discussed. 

Fri, Jun 18, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Informal Group Meeting
Thu, Jun 17, '10
16:00 - 17:00
CRiSM Seminar - Adrian Bowman (Glasgow)
A1.01

Prof Adrian Bowman, University of Glasgow

 Surfaces, shapes and anatomy
 
Three-dimensional surface imaging, through laser-scanning or stereo-photogrammetry, provides high resolution data defining the shape of objects.  In an anatomical setting this can provide invaluable quantitative information, for example on the success of surgery.  Two particular applications are in the success of breast reconstruction and in facial surgery following conditions such as cleft lip and palate.  An initial challenge is to extract suitable information from these images, to characterise the surface shape in an informative manner. Landmarks are traditionally used to good effect but these clearly do not adequately represent the very much richer information present in each digitised images. Curves with clear anatomical meaning provide a good compromise between informative representations of shape and simplicity of structure.  Some of the issues involved in analysing data of this type will be discussed and illustrated. Modelling issues include the measurement of asymmetry and longitudinal patterns of growth.
 
A second form of surface data arises in the analysis of MEG data which is collected from the head surface of patients and gives information on underlying brain activity.  In this case, spatiotemporal smoothing offers a route to a flexible model for the spatial and temporal locations of stimulated brain activity.

  

Fri, Jun 11, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
John Aston (Warwick)
Fri, Jun 4, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Informal Group Meeting
Thu, Jun 3, '10
16:00 - 18:00
CRiSM Seminar - Idris Eckley (Lancaster)
A1.01
Idris Eckley (Lancaster)
Wavelets - the secret to great looking hair?

Texture is the visual character of an image region whose structure is, in some sense, regular, for example the appearance of a woven material. The perceived texture of an image depends on the scale at which it is observed. In this talk we show how wavelet processes can be used to model and analyse texture structure. Our wavelet texture models permit the classification of images based on texture and reveal important information on differences between subtly different texture types. We provide examples, taken from industry, where wavelet methods have enhanced the classification of images of hair and fabrics.
Fri, May 28, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Mahadevan Ganesh (Edinburgh)
Thu, May 27, '10
16:00 - 18:00
CRiSM Seminar - William Astle (Imperial)
A1.01
William Astle (Imperial)

A Bayesian model of NMR spectra for the deconvolution and quantification of metabolites in complex biological mixtures

Wed, May 26, '10
08:00 - 09:00
Seminar from Warwick back to Melbourne
Digital Laboratory Auditorium

Ann Nicholson (Monash University)
Bayesian Networks for Biosecurity Risk Assessment

Bayesian networks (BNs) are rapidly becoming a tool of choice for ecological and environmental modelling and decision making. By combining a graphical representation of the dependencies between variables with probability theory and efficient inference algorithms, BNs provide a powerful and flexible tool for reasoning under uncertainty.  The popularity of BNs is based on their ability to reason both diagnostically and predictively, and to explicitly model causal interventions and cost-benefit trade-offs.

In Australia, current biosecurity risk assessments are typically qualitative, combining assessment across the stages of importatation, distribution, entry, establishment and spread. In this seminar, I will show a BN that directly models the current qualitative method.  I'll then adapt the BN to explicitly model the volume of infestation, adding clarity and precision.  I will demonstrate how more complex BNs can explicitly model the factors influencing each stage, and can be extended with management decisions and cost functions for decision making.

Fri, May 21, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Omiros Papaspiliopoulos (Universitat Pompeu Fabra)
Thu, May 20, '10
16:00 - 17:00
CRiSM Seminar - Claudia Kirch (Karlsruhe)
A1.01
Claudia Kirch (Karlsruhe)
Resampling Methods in Change-Point Analysis
Real life data series are frequently not stable but exhibit changes in parameters at unknown time points. We encounter changes (or the possibility thereof) everyday in such diverse fields as economics, finance, medicine, geology, physics and so on. Therefore the detection, location and investigation of changes is of special interest. Change-point analysis provides the statistical tools (tests, estimators, confidence intervals). Most of the procedures are based on distributional asymptotics, however convergence is often slow -- or the asymptotic does not sufficiently reflect dependency. Using resampling procedures we obtain better approximations for small samples which take possible dependency structures more efficiently into account.
In this talk we give a short introduction into change-point analysis. Then we investigate more closely how resampling procedures can be applied in this context. We have a closer look at a classical location model with dependent data as well as a sequential location test, which has become of special interest in recent years.
Wed, May 19, '10
14:00 - 15:00
CRiSM Seminar - Petros Dellaportas (Athens University)
A1.01
Petros Dellaportas (Athens University of Economics and Business)
Control variates for reversible MCMC samplers
A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive, consistent MCMC estimators are derived for these optimal coefficients. All methodological and asymptotic arguments are rigorously justified. Numerous MCMC simulation examples from Bayesian inference applications demonstrate that the resulting variance reduction can be quite dramatic.
Fri, May 14, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Informal Group Meeting
Thu, May 13, '10
16:00 - 17:00
CRiSM Seminar - Federico Turkheimer (Imperial)
A1.01
Federico Turkheimer (Imperial)

Title: Higher Mental Ability: A Matter of Persistence?
Abstract: Executive function is thought to originate in the dynamics of frontal cortical networks of the human brain. We examined the dynamic properties of the blood oxygen level-dependent (BOLD) time-series measured with fMRI within the prefrontal cortex to test the hypothesis that temporally persistent neural activity underlies executive performance in normal controls doing executive tasks. A numerical estimate of signal persistence, derived from wavelet scalograms of the BOLD time-series and postulated to represent the coherent firing of cortical networks, was determined and correlated with task performance. We further tested our hypothesis on traumatic brain injury subjects that present with mild diffuse heterogenous injury but common executive dysfunction, this time using a resting state experimental condition.
 
11:00 - 13:00
Ann Nicholson - Workshop 2
C1.06
Applications of Bayesian Networks
Fri, May 7, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
Informal Group Meeting
Fri, Apr 30, '10
12:00 - 13:00
Applied Maths & Stats Seminar
B3.02 (Maths)
David White (Warwick)

Thu, Apr 29, '10
16:00 - 17:00
CRiSM Seminar - Ann Nicholson (Monash)
A1.01

Ann Nicholson (Monash)

Incorporating expert knowledge when learning Bayesian network structure: Heart failure as a case study

Bayesian networks (BNs) are rapidly becoming a leading technology in applied Artificial Intelligence (AI), with medicine one of its most popular application area.  Both automated learning of BNs and expert elicitation have been used to build these networks, but the potentially more useful combination of these two methods remain underexplored. In this seminar, I will present a case study of this combination using public-domain data for heart failure. We run an automated causal discovery system (CaMML), which allows the incorporation of multiple kinds of prior expert knowledge into its search, to test and compare unbiased discovery with discovery biased with different kinds of expert opinion. We use adjacency matrices enhanced with numerical and colour labels to assist with the interpretation of the results.  These techniques are presented within a wider context of knowledge engineering with Bayesian networks
 (KEBN). 
Fri, Mar 26, '10
14:00 - 16:00
CRiSM Seminar - David Findley (US Census Bureau)
A1.01

David Findley (US Census Bureau)

Two improved Diebold-Mariano test statistics for comparing the forecasting ability of incorrect time series models

We present and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h -step-ahead forecasts than another, as measured by the difference of approximations to their asymptotic mean square forecast errors. The two statistics differ in the variance estimate whose square root is the statistic's denominator. Both variance estimates are consistent even when the ARMA components of the models considered are incorrect. Our principal statistic's variance estimate accounts for parameter estimation. Our simpler statistic's variance estimate treats parameters as fixed. The broad consistency properties of these estimates yield improvements to what are known as tests of Diebold and Mariano (1995) type. These are tests whose variance estimates treat parameters as fixed and are generally not consistent in our context.

We describe how the new test statistics can be calculated algebraically for any pair of ARIMA models with the same differencing operator. Our size and power studies demonstrate their superiority over the Diebold-Mariano statistic. The power study and the empirical study also reveal that, in comparison to treating estimated parameters as fixed, accounting for parameter estimation can increase power and can yield more plausible model selections for some time series in standard textbooks.

(Joint work with Tucker McElroy)

Thu, Mar 18, '10
16:00 - 18:00
CRiSM Seminar - Prakash Patil (Birmingham)
A1.01

Prakash Patil (University of Birmingham)
Smoothing based Lack-of-Fit (or Goodness-of-Fit) Tests

To construct a nonparametric (smoothing-based) test of lack-of-fit, one measures one way or other, the discrepancy between a smooth estimator of the unknown curve and the hypothesised curve. Although there are many possible choices for measuring this discrepancy, for being technically most easy to deal with, the lack-of-fit tests based on the ISE seem to have received the most(?) attention. But since a test based on the ISE requires the estimation of the unknown curve, its ability to distinguish between the null model and the departures from the null model is linked to the smoothing parameter that one chooses to estimate the curve. Whereas, if one takes a local view and then constructs a test, one can show that the test has better power properties. And although the performance of the test is still linked to the smoothing parameter, the choice of smoothing parameter will now be dictated by the `testing’ aspect of the problem rather than be driven by the estimation of the unknown curve. In this talk, we will mainly use regression quantile curves to illustrate the above points but will show that this procedure could be used for density and hazard rate curves.
Thu, Mar 4, '10
16:00 - 18:00
CRiSM Seminar - Jeremy Taylor (Michigan)
A1.01
Jeremy Taylor, University of Michigan
Individualized predictions of prostate cancer recurrence following radiation therapy
In this talk I will present a joint longitudinal-survival statistical model for the pattern of psa values and clinical recurrence for data from patients following radiation therapy for prostate cancer. A random effects model is used for the longitudinal psa data and a time dependent proportional hazards model is used for clinical recurrence of prostate cancer. The model is implemented on a website, psacalc.sph.umich.edu , where patients or doctors can enter a series of psa values and obtain a prediction of future disease progression. Details of the model estimation and validation will be described and the website calculator demonstrated.
Thu, Feb 25, '10
16:00 - 18:00
CRiSM Seminar - Vincent Macaulay (Glasgow)
A1.01
Vincent Macaulay, Dept of Statistics, University of Glasgow
Inference of migration episodes from modern DNA sequence variation
One view of human prehistory is of a set of punctuated migration events across space and time, associated with settlement, resettlement and discrete phases of immigration. It is pertinent to ask whether the variability that exists in the DNA sequences of samples of people living now, something which can be relatively easily measured, can be used to fit and test such models. Population genetics theory already makes predictions of patterns of genetic variation under certain very simple models of prehistoric demography. In this presentation I will describe an alternative, but still quite simple, model designed to capture more aspects of human prehistory of interest to the archaeologist, show how it can be rephrased as a mixture model, and illustrate the kinds of inferences that can be made on a real data set, taking a Bayesian approach.
Thu, Feb 18, '10
16:00 - 18:00
CRiSM Seminar - Theo Kypraios (Nottingham)
A1.01
Theo Kypraios (Nottingham)
A novel class of semi-parametric time series models: Construction and Bayesian Inference
Abstract
--------
In this talk a novel class of semi-parametric time series models will be presented, for which we can specify in advance the marginal distribution of the observations and then build the dependence structure of the observations around them by introducing an underlying stochastic process termed as 'latent branching tree'. It will be demonstrated how can we draw Bayesian inference for the model parameters using Markov Chain Monte Carlo methods as well as Approximate Bayesian Computation methodology. Finally a real dataset on genome scheme data will be fitted to these models and we will also discuss how this kind of models can be used in modelling Internet traffic.
Thu, Feb 11, '10
16:00 - 18:00
CRiSM Seminar - Alexander Schied (Mannheim)
A1.01
Alexander Schied (Mannheim)
Mathematical aspects of market impact modeling
Abstract: In this talk, we discuss the problem of executing large orders in illiquid markets so as to optimize the resulting liquidity costs. There are several reasons why this problem is relevant. On the mathematical side, it leads to interesting  nonlinearity effects that arise from the price feedback of  strategies. On the economical side, it helps  understanding which market impact models are viable, because the analysis of order execution provides a test for the existence of undesirable properties of a model. In the first part of the talk, we present market impact models with transient price impact, modeling the resilience of electronic limit order books. In the second part of the talk, we consider the Almgren-Chriss market impact model and analyze the effects of risk aversion on optimal strategies by using stochastic control methods. In the final part, we discuss effects that occur in a multi-player equilibrium.
Thu, Jan 28, '10
16:00 - 17:00
CRiSM Seminar - Jan Palczewski
A1.01
Dr Jan Palczewski (University of Leeds)
Why Markowitz portfolio weights are so volatile?
Markowitz theory of asset allocation is one of very few research ideas that made it into practical finance. Yet, its investment recommendations exhibit incredible sensitivity to even smallest variations in the estimation horizon or estimation techniques. Scientists as well as practitioners have put enormous effort into stabilizing the estimators of portfolios (with moderate success, according to some). However, there seems to be no simple quantitative method to measure the portfolio stability. In this talk, I will derive
analytical formulas that relate the mean and the covariance matrix of asset returns with the stability of portfolio composition. These formulas allow for the indentification of main culprits of worse-than-expected performance of the Markowitz framework. In particular, I will question the common wisdom that puts the main responsibility on estimation errors of the mean.

This research is a spin-off of a consultancy project at the University of Warsaw regarding the allocation of the foreign reserves of Polish Central Bank.
Thu, Dec 10, '09
16:00 - 17:30
CRiSM/Stats Seminar - Siem Jan Koopman
A1.01
Siem Jan Koopman
Free University Amsterdam
 
Title: Dynamic factor analysis and the dynamic modelling of the yield curve of interest rates.
 
Abstract:
A new approach to dynamic factor analysis by imposing smoothness restrictions on the factor loadings is proposed. A statistical procedure based on Wald tests that can be used to find a suitable set of such restrictions is presented. These developments are presented in the context of maximum likelihood estimation. The empirical illustration concerns term structure models but the methodology is also applicable in other settings. An empirical study using a data set of unsmoothed Fama-Bliss zero yields for US treasuries of different maturities is performed. The general dynamic factor model with and without smooth loadings is considered in this study together with models that are associated with Nelson-Siegel and arbitrage-free frameworks. These existing models can be regarded as special cases of the dynamic factor model with restrictions on the model parameters. Statistical hypothesis tests are performed in order to verify whether the restrictions imposed by the models are supported by the data. The main conclusion is that smoothness restrictions can be imposed on the loadings of dynamic factor models for the term structure of US interest rates.
[Joint work with Borus Jungbacker and Michel van der Wel]
Thu, Dec 3, '09
16:00 - 18:00
CRiSM Seminar - Serge Guillas (UCL)
A1.01

Serge Guillas (UCL)
Bivariate Splines for Spatial Functional Regression Models
We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, in various situations where both the explanatory variable and the noise can be unbounded and dependent. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct  least squares estimators of the regression function with a penalization term. Under the assumptions that the regressors in the sample span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the US that illustrates the predictive skills of the method.
Finally, we present recent results of long-term seabed forecasting using this technique.

Fri, Nov 27, '09
14:00 - 16:00
CRiSM Seminar - Peter Muller
A1.01
Peter Müller
A DEPENDENT POLYA TREE MODEL
with Lorenzo Trippa and Wes Johnson

We propose a probability model for a family of unknown distributions indexed with covariates. The marginal model for each distribution is a Polya tree prior. The proposed model introduces the desired dependence across the marginal Polya tree models by defining dependent random branching probabilities of the unknown distributions.

An important feature of the proposed model is the easy centering of the nonparametric model around any parametric regression model.  This is important for the motivating application to the proportional hazards (PH) model. We use the proposed model to implement nonparametric inference for survival regression. The proposed model allows us to center the nonparametric prior around parametric PH structures.  In contrast to many available models that restrict the non-parametric extension of the PH model to the baseline hazard, the proposed model defines a family of random probability measures that are a priori centered around the PH model but allows any other structure.  This includes, for example, crossing hazards, additive hazards, or any other structure as supported by the data.

Thu, Nov 19, '09
16:00 - 17:30
CRiSM Seminar - Anna Gottard
A1.01

Anna Gottard (Florence)
Graphical models for homologous factors
Abstract: Homologous factors are factors measured with the same categorical scale. They are commonly encountered in matched pairs studies, in attitudinal research where subjects’ opinions about some issue are observed under several conditions, or in longitudinal studies that repeatedly observe whether a condition is present at various times. In these cases, it can happen that the contingency table cross classifying the homologous factors shows a special structure, typically captured by symmetry and quasi-symmetry models. In this talk, I will present a class of graphical log linear models having symmetry and quasi-symmetry models as particular cases, and allowing situations of conditional independence and the presence of non-homologous factors. This class of models can be associated with a graph with coloured edges and nodes. (This is partially joint work with G.M. Marchetti and A. Agresti).

Tue, Nov 17, '09
16:00 - 18:00
CRiSM Seminar - James Curran
D1.07 Complexity Seminar Rm

James Curran (Auckland)

Some issues in modern forensic DNA evidence interpretation

The forensic biology community has adopted new DNA typing technology relatively quickly as it has evolved over the last twenty years. However, the adoption of the statistical methodology used for the interpretation of this evidence has not been as fast. In this talk I will discuss classical forensic DNA interpretation and how it the changes in technology  and thinking have led to challenges to the way we interpret evidence. I will present some relatively new models for evidence interpretation, and discuss future directions. This talk is aimed at a general audience.

Wed, Nov 11, '09
16:00 - 18:00
CRiSM Seminar - Tomasz Schreiber
A1.01

Professor Tomasz Schreiber (Nicolaus Copernicus University)
Polygonal Markov fields in the plane
Abstract: Polygonal Markov fields (PMFs), originally introduced by Arak, Clifford and Surgailis, can be regarded as random ensembles of non-intersecting planar polygonal contours with interaction determined by a rather flexible class of potentials. Not unexpectedly, such models share a number of important properties with the two-dimensional Ising model, including Ising-like phase transitions, spontaneous magnetisation and low temperature phase separation (Wulff construction). On the other hand, the polygonal fields exhibit remarkable features of their own, such as consistency property and explicit expressions for many crucial numeric and functional characteristics (free energy, correlation functions, integral geometric characteristics). Arguably the most important property of polygonal fields is that they admit a rich class of graphical constructions, all yielding the same field and often used as a crucial tool in theoretical developments on PMFs. In this talk we take the algorithmic graphical constructions as the starting point for defining the polygonal Markov fields, rather than the usual Gibbsian formalism. This point of view is compatible with applications of the PMFs for Bayesian image segmentation which we shall present (joint work with M.N.M. van Lieshout, R. Kluszczynski and M. Matuszak). Further, we shall also discuss our latest theoretical developments made possible by this approach, examples including the evaluation of higher order correlation functions, factorisation theorems and duality theory, where the dual object - the polygonal web - arises as the union of interacting critical branching polygonal walks in the plane. We shall conclude the talk indicating existing open problems and conjectures on the PMFs.

Thu, Nov 5, '09
15:00 - 18:00
Warwick Oxford Joint Seminar (at Warwick)
PS1.28

Oxford-Warwick Joint Seminar (2 talks)

Speaker 1:  Andrew Stuart (University of Warwick)

Title: MCMC in High Dimensions

Abstract: Metropolis based MCMC methods are a flexible tool for sampling a wide variety of complex probability distributions. Nonetheless, their effective use depends very much on careful tuning of parameters, choice of proposal distribution and so forth. A thorough understanding of these issues in high dimensional problems is particularly desirable as they can be critical to the construction of a practical sampler.
 
In this talk we study MCMC methods based on random walk, Langevin and Hybrid Monte Carlo proposals, all of which are based on the discretization of a (sometimes stochastic) differential equation. We describe how to scale the time-step in this discretization to achieve optimal efficiency, and compare the resulting computational cost of the different methods. We initially confine our study to target distributions with a product structure but then show how the ideas may be extended to a wide class of non-product measures arising in applications; these arise from measures on a Hilbert space which are absolutely continuous with respect to a product measure.  We illustrate the ideas through application to a range of problems arising in molecular dynamics and in data assimilation in the ocean-atmosphere sciences.
 
The talk will touch on various collaborations with Alex Beskos (UCL), Jonathan Mattingly (Duke), Gareth Roberts (Warwick), Natesh Pillai (Warwick) and Chus Sanz-Serna (Valladolid).


2.  Tom Nichols (University of Warwick and University of Oxford)


A Hierarchical Spatial Bayesian Model for Multisubject Functional MRI Data

Standard practice in Functional Magnetic Resonance Imaging (fMRI) is to use a 'mass-univariate' model, where linear models are fit independently at each spatial location.  A fundamental assumption of this approach is that the image data has been spatially warped so that anatomy of each subject's brain aligns.  In practice, even after the best anatomical warping, practitioners find that individual subjects have activations in different locations (though still in the same general anatomic area).  Within the mass-univariate framework the only recourse is to spatially smooth the data, causing the effects to be blurred out and allowing areas of common activation to be detected. Our approach is to fit a Bayesian hierarchical spatial model to the unsmoothed data.  We model each subject's data with individual activation centres which are assumed to cluster about population centres.  Our model thus allows and explicitly estimates intersubject heterogeneity in location and yet also makes precise inferences on the activation location in the population.  We demonstrate the method on simulated and real data of a visual working memory experiment.
[joint with Lei Xu, Department of Biostatistics, Vanderbilt University, and Timothy Johnson, Department of Biostatistics, University of Michigan.]

Thu, Oct 22, '09
16:00 - 18:00
CRiSM Seminar - Roman Belavkin
A1.01

Roman Belavkin (Middlesex University)

The effect of information constraints on decision-making and economic behaviour

Economic theory is based on the idea of rational agents acting according to their preferences.  Mathematically, this is represented by maximisation of some utility or the expected utility function, if choices are made under uncertainty.  Although this formalism has become dominant in optimisation, game theories and even AI, there is a degree of scepticism about the expected utility representation, especially among behavioural economists who often use paradoxical counter-examples dating back as far as Aristotle.  I will try to convince you that many of these paradoxes can be avoided if the problem is treated from a learning theory point of view, where information constraints are explicitly taken into account.  I will use methods of functional and convex analyses to demonstrate geometric interpretation of the solution of an abstract optimal learning problem, and demonstrate how this solution explains the mismatch between the normative and behavioural theories of decision-making.

Fri, Oct 16, '09
14:00 - 16:00
CRiSM Seminar - Arnaud Doucet
A1.01

Arnaud Doucet (ISM)

Forward Smoothing using Sequential Monte Carlo with Application to Recursive Parameter Estimation

 Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose new SMC algorithms to compute the expectation of additive functionals recursively. Compared to the standard path space SMC estimator whose asymptotic variance increases quadratically with time even under favourable mixing assumptions, the asymptotic variance of the proposed SMC estimates only increase linearly with time. We show how this allows us to perform recursive parameter estimation using SMC algorithms which do not not suffer from the particle path degeneracy problem.

 

Joint work with P. Del Moral (INRIA Bordeaux) & S.S. Singh (Cambridge University.

Thu, Oct 8, '09
16:00 - 17:30
CRiSM Seminar - Peter Diggle
A1.01

Peter Diggle (Lancaster University and Johns Hopkins University)

Statistical Modelling for Real-time Epidemiology

Thu, Jun 25, '09
16:00 - 17:00
CRiSM Seminar - Dr Frederic Ferraty
A1.01

Dr Frederic Ferraty, University of Toulouse, France

Most-predictive design points for functional data predictors

(In coll. with Peter Hall and Phillipe Vieu)

Functional data analysis (FDA) has found application in a great many fields, including biology, chemometrics, econometrics, geophysics, medical sciences, pattern recognization....  For instance a sample of curves or a sample of surfaces is a special case of functional data.  In the example of near infrared (NIR) spectroscopy, X(t) denotes the absorbance of the NIR spectrum at wavelength t.  The observation of X(t) for a discrete but large set of values (or design points) t produces what is called a spectrometric curve.  A standard chemometrical dataset is that where X(t) corresponds to the NIR spectrum of a piece of meat and where a scalar response Y denotes a constituent of the piece of meat (eg, fat or moisture).

Here, we are interested in regressing a scalar response Y on a functional predictor X(t) where t belongs to a discrete but large set I of "design points" (hundreds or thousands).  From now on, one sets X:={X(t);t in I}.  It is of practical interest to know which design points of t, have greatest influence on the response, Y.  In this situation, we propose a method for choosing a small subset of design points to optimize prediction of a response variable, Y.  The selected design points are referred to as the most predictive design points, or covariates, and are computed using information contained in a set of independent observations (X_i,Y_i) of (X,Y).  The algorithm is based on local linear regression, and calculations can be accelerated using linear regression to preselect design points.  Boosting can be employed to further improve predictive performance.  We illustrate the usefulness of our ideas through examples drawn from chemometrics, and we develop theoretical arguments showing that the methodology can be applied successfully in a range of settings.

Thu, Jun 11, '09
16:00 - 17:00
CRiSM Seminar - Dr Daniel Jackson
A1.01

Dr Daniel Jackson, MRC Biostatistics Unit

How much can we learn about missing data?  An exploration of a clinical trial in psychiatry

by Dan Jackson, Ian R White and Morven Leese

When a randomised controlled trial has missing outcome data, any analysis is based on untestable assumptions, for example that the data are missing at random, or less commonly on other assumptions about the mising data mechanism.  Given such assumptions, there is an extensive literature on suitable analysis methods.  However, little is known about what assumptions are appropriate.  We use two sources of ancillary data to explore the missing data mechanism in a trial of adherence therapy in patients with schizophrenia: carer-reported (proxy) outcomes and the number of contact attempts.  This requires making additional assumptions whose plausibility we discuss.  We also perform sensitivity analyses to departures from missing at random.  Wider use of techniques such as these will help to inform the choice of suitable assumptions for the analysis of randomised controlled trials.

Tue, Jun 9, '09
16:00 - 17:00
CRiSM Seminar - Dr Pulak Ghosh
A1.01

Dr Pulak Ghosh, Georgia State University, USA

Joint Modelling of Multivariate Longitudinal Data for Mixed Responses with Application to Multiple Sclerosis Data

Multiple sclerosis (MS) is one of the most chronic neurological diseases in young adults with around 2.5 million affected individuals worldwide (Compston 2006).  The most common presenting symptoms are inflammation of the optic nerve, weakness, sensory disturbances, gait disturbances and bladder dysfunction.  So far only standard analysis methodology to estimate risks for relapse occurence has been used.  This includes mostly single endpoint survival analysis in which MRI information is shrunken to baseline values or aggregated measures such as means.  In the present analysis we aim to establish a model that llows the description and prediction of occurence of relapses by considering processes in the brain (visualized on T1 and T2 weighted MRI) simultaneously.  These complex processes, together with clinical baseline infromation, have never been considered in one model so far.  We will use our model to evaluate strength of dependencies of multivariate longitudinal MRI measures with the occurrence of MS relapses.

Thu, Jun 4, '09
16:00 - 17:00
CRiSM Seminar - Dr Chendi Zhang
A1.01

Dr Chendi Zhang, Warwick Business School

Information Salience, Investor Sentiment and Stock Returns : The Case of British Soccer Betting

Soccer clubs listed on the London Stock Exchange provide a unique way of testing stock price reactions to different types of news.  For each firm, two pieces of information are released on a weekly basis : experts' expectations about game outcomes through the betting odds, and the game outcomes themselves.  The stock market reacts strongly to news about game results, generating significant abnormal returns and trading volumes.  We find evidence that the abnormal returns for the winning teams do not reflect rational expectations but are high due to overreactions induced by investor sentiment.  This is not the case for losign teams.  There is no market reaction to the release of new betting information although these betting odds are excellent predictors of the game outcomes.  Ths discrepancy between the strong market reaction to game results and the lack of reaction to betting odds may not only be the result from overreaction to game results but also from the lack of informational content or information salience of the betting information.  Therefore, we also examine whether betting information can be used to predict short-run stock returns subsequent to the games.  We reach mixed results: we conclude that investors ignore some non-salient public information such as betting odds, and betting information predicts a stock price overreaction to game results which is influenced by investors' mood (especially when the teams are strongly expected to win).

Thu, May 14, '09
16:00 - 17:00
CRiSM Seminar - Prof Howell Tong
A1.01

Prof Howell Tong, LSE & Hong Kong University

Time Reversibility of Multivariate Linear Time Series

In the time series literature, time reversibility is often assumed either explicitly (if honest) or implicitly (if less so).  In reality, time reversibility is the exception rather than the rule.  The situation with multivariate time series is much more exotic as this seminar will explore.

Thu, May 7, '09
16:00 - 17:00
CRiSM Seminar - Prof T Bandyopadhyay
A1.01

Professor Tathagata Bandyopadhyay, Indian Institute of Management, Ahmedabad, India

Testing Equality of Means from Paired Data When The Labels Are Missing

Suppose (Xi, Y9) i=1,..,n represent a random sample of size n from a bivariate normal population.  Suppose for some reason the labels in each pair are missing.  We consider the problem of testing the null hypothesis of equality of means based on such a messy data set.  We will cite a few practical instances when such a situation may arise.  Naturally, standard t- test cannot be applied here since one can not label the components of each pair by 'X' or 'Y'.  Instead, the observable pairs are (Mi, mi), i=1, ...n, where Mi = max(Xi, Yi) and mi = min(Xi, Yi).  We will talk about a number of large sample tests based on (Mi, mi) for testing the above hypothesis.

 

Thu, Apr 30, '09
16:00 - 17:00
CRiSM Seminar - Dr David MacKay
MS.03

David MacKay, University of Cambridge

Hands-free Writing

Keyboards are inefficient for two reasons: they do not exploit the predictability of normal language; and they waste the fine analogue capabilities of the user's muscles.  I describe Dasher, a communications system designed using information theory.  A person's gestures are a source of bits, and the sentences they wish to communicate are the sink.  We aim to maximise the number of bits per second conveyed from user into text.

Users can achieve single-finger writing speeds of 35 words per minute and hands-free writing speeds of 25 words per minute.

Dasher is free spftware, and it works in over one hundred languages.

Thu, Apr 23, '09
16:00 - 17:00
CRiSM Seminar - Prof Hans Kuensch
A1.01

Prof Hans Kuensch, ETH Zurich

Ensemble kalman filter versus particle filters

With high dimensional state space, particle filters usually behave badly.  In atmospheric science, the ensemble Kalman filter is used instead which assumes a linear Gaussian observation and a Gaussian prediction distribution.  I will discuss some open problems from a statistical perspective.

Tue, Mar 17, '09
11:00 - 12:00
CRiSM Seminar - Dr Cristiano Varin
A1.01

Dr Cristiano Varin, Ca' Foscari University, Venice

Marginal Regression Models with Stationary Time Series Errors

This talk is concerned with regression analysis of serially dependent non-normal observations.  Stemming from traditional linear regression models with stationary time series errors, a class of marginal models that can accommodate responses of any type is presented.  Model fitting is performed either by exact or simulated maximum likelihood whether the responses is continuous or not.  Computational aspects are described in detail.  Real data applications to time series of counts are considered for illustration.  The talk is based on collaborative work with Guido Masarotto, University of Padova.

Thu, Mar 12, '09
16:00 - 17:00
CRiSM Seminar - Dr Peter Craig
A1.01

Dr Peter Craig, University of Durham

Multivariate normal orthant probabilities - geometry, computation and application to statistics

The multivariate normal distribution is the basic model for multivariate continuous variability and uncertainty and its properties are intrinsically interesting.  The orthant probablility (OP) is the probability that each component is positive and is of practical importance both as the generalisation of tail probability and as the likelihood function for multivariate probit models.  Efficient quasi-Monte Carlo methods are available for approximation of OPs but are unsuitable for high-precision calculations. However, accurate calculations are relatively straightforward for some covariance structures other than independence.  I shall present the geometry of two ways to express general OPs in terms of these simpler OPs, discuss the computational consequences and briefly illustrate the application of these methods to a classic application of multivariate probit modelling.

Thu, Mar 5, '09
16:00 - 17:00
CRiSM Seminar - Dr Catherine Hurley
A1..01

Dr Catherine Hurley, National University of Ireland, Maynooth

Composition of statistical graphics: a graph-throretic perspective

Visualization methods are crucial in data exploration, presentation and modelling.  A carefully chosen graphic reveals information about the data, assisting the viewer in comparing and relating variables, cases, groups, clusters ormodel fits.  A statistical graphic is composed of display components whose arrangement (in space or time) facilitates thses comparisons.  In this presentation, we take a graph-theoretic prespective ot the graphical layout problem.  The basic idea is that graphical layouts are essentially traversals of appropriately constructed mathematical graphs.  We explore the construction of familiar scatterplot matrices and parallel coordinate displays from this perspective.  We present graph traversal algorithms tailored to the graphical layout prolem.  Novel applications range from a new display for pairwise comparison of treatment groups, to a guided parallel coordinate display and on to a road map for dynamic exploration of high-dimensional data.

Fri, Feb 27, '09
15:00 - 16:00
CRiSM Seminar - Victor M Panaretos
A1.01

Victor M Panaretos, Institute of Mathematics, Ecole Polytechnique Federale de Lausanne

Modular Statistical Inference in Single Particle Tomography

What can be said about an unknown density function on $\mathbb{R}^n$ given a finite collection of projections onto random and unknown hyperplanes? This question arises in single particle electron microscopy, a powerful method that biophysicists employ to learn about the structure of biological macromolecules. The method images unconstrained particles, as opposed to particles fixed on a lattice (crystallography) and poses a variety of problems. We formulate and study statistically the problem of determining a structural model for a biological particle given random projections of its Coulomb potential density, observed through the electron microscope. Although unidentifiable (ill-posed), this problem can be seen to be amenable to a consistent modular statistical solution once it is viewed through the prism of shape theory.

Thu, Feb 26, '09
16:00 - 17:00
CRiSM Seminar - Dr Abhir Bhalerao
A1.01

Dr Abhir Bhalerao, University of Warwick

Automatic Screening for Microaneurysms in Digital Images

Diabetic retinopathy is one of the major causes of blindness.  However, diabetic retinopathy does not usually casuse a loss of sight until it has reached an advanced stage.  The earliest signs of the disease are microaneurysms (MA) which appear as small red dots on retinal fundus images.  Various screening programmes have been established in the UK and other coutries to collect and assess images on a regular basis, especially in the diabetic population.  A considerable amount of time and money is spent in manually grading these images, a large percentage of which are normal.  By automatically identifying the normal images, the manual workload and costs could be reducced greatly while increasing the effectiveness of the screening programmes.  A novel method of microaneurysm from digital retinal screening images is presented.  It is based on image filtering using complex-valued circular-symmetric filters, and an eigen-image, morphological analysis of the candidate regions to reduce the false-positive rate.  The image processing algorithms will be presented with evaluation on a typical set of 89 images from a published database.  Teh resulting method is shown to have a best operating sensitivity of 82.6% at a specificity of 80.2% which makes is useful for screening.  The results are discussed in the context of a model of visual search and the ROC curves that it can predict.

Mon, Feb 23, '09
15:00 - 16:00
CRiSM Seminar - Dr Yvonne Ho
A1.01

Dr Yvonne Ho, Imperial College London

Conditional accuracy and robustness

We shall review the classical conditionality principle in statistics and study conditional inference procedures under nonparametric regression models, conditional on the observed residuals.  As revealed from the title of the talk, we shall consider two issues: inference accuracy and robustness.  An innovative procedure using a smoothing technique in conjunction with configural polysampling will be presented.

Thu, Feb 19, '09
16:00 - 17:00
CRiSM Seminar - Dr Jian Qing Shi
A1.01

Dr Jian Qing Shi, University of Newcastle

Curve Prediction and Clustering using Mixtures of Gaussian Process Functional Regression Models

The problem of large data is one major statistical challenges, for example, more and more data are generated from subjects with different backgrounds at an incredible rate in one of our biomechanical project as well as some many other examples.  For such functional/longitudinal data, it is more flexible and efficient to treat them as curves, and flexible mixture models are capable of capturing variation and biases for the data generated from different resources.  Mixture models are also applicable to classification and clustering of the data.

In this talk, I will first introduce a nonparametric Gaussian process functional regression (GPFR) model, and then discuss how to extend to a mixture model to address the problem of heterogeneity with multiple data types.  A mew method will be presented for modelling functional data with 'spatially' indexed data, ie, the heterogeneity is dependent on factors such as region and individual patient's information.  Nonparametric and functional mixture models have also been developed for curve clustering for some very complex systems which the response curves may depend on a number of functional and non-functional covariates.  Some numerical results with simulations study and real applications will also be present.

Thu, Jan 29, '09
16:00 - 17:00
CRiSM Seminar - Dr Igor Pruenster
A1.01 - Zeeman Building

Di Finetti Afternoon, two seminars on Non-Parametric Bayesian Analysis, 2-5pm

Dr Igor Pruenster (Torino, Italy)

Asymptotics for posterior hazards

A popular Bayesian nonpaametric approach to survival analysis consists in modelling hazard rates as kernel mixtures driven by a completely random measure.  A comprehensive analysis of the asymptotic behaviour of such models is provided.  Consistency of the posterior distribution is investigated and central limit theorems for both linear and quadratic functionals of the posterior hazaed rate are derived.  The general results are then specialized to various specific kernels and mixing measures, thus yielding consistency under minimal conditions and near central limit theorems for the distribution of functionals.

Joint work with P. De Blasi and G. Peccati

 
14:30 - 15:30
CRiSM Seminar - Dr Antonio Lijoi
A1.01 - Zeeman Building

Di Finetti Afternoon, two seminars on Non-Parametric Bayesian Analysis, 2-5pm

Dr Antonio Lijoi (Pavia, Italy)

Priors for vectors of probability distributions

In this talk we describe the construction of a nonparametric prior for vectors of probablility distributions obtained by a suitable transformation of completely random measures.  The dependence between random probability distributions by a Levy copula.  A first example that will be presented concerns a prior for a pair of survival functions and it will be used to model two-sample data: a posterior characterization, conditionally on possibly right-censored data, will be provided.  Then, a vector of random probabilities, with two-parameter Poisson-Dirichlet marginals, is introduced.

Thu, Jan 22, '09
16:00 - 17:00
CRiSM Seminar
Room A1.01, Zeeman Building

Dr Laura Sangalli, Politecnico di Milano

Title : Efficient estimation of curves in more than one dimension by free-knot regression splines, with applications to the analysis of 3D cerebral vascular geometries.

Abstract : We deal with the problem of efficiently estimating a 3D curve and its derivatives, starting from a discrete and noisy observation of the curve.  We develop a regression technique based on free-knot splines, ie. regression splines where the number and position of knots are not fixed in advance but chosen in a way to minimize a penalized sum of squared errors criterion.  We thoroughly compare this technique to a classical regression method, local polynomial smoothing, via simulation studies and application to the analysis of inner carotid artery centerlines (AneuRisk Project dataset).  We show that 3D free-knot regression splines yield more accurate and efficient estimates.

 Joint work with Piercesare Secchi and Simone Vantini.

Fri, Dec 12, '08
12:00 - 13:00
Joint CRiSM/Applied Maths/Stats Seminar
A1.01
Professor Jeff Rosenthal, University of Toronto
Adaptive MCMC
Thu, Nov 27, '08
16:00 - 17:00
CRiSM Seminar - Anthony Reveillac
A1.01
Anthony Reveillac
Humboldt University - Berlin

 

Stein estimators and SURE shrinkage estimation for Gaussian processes using the Malliavin calculus

In this talk we present a construction of Stein type estimators for the drift of Gaussian processes using the Malliavin integration by parts formula. Then we construct an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise using the local and occupation times of Gaussian processes. This talk is based on joint works with Nicolas Privault.

Wed, Nov 12, '08
16:00 - 17:00
Joint Stats/Econometrics Seminar: Sylvia Fruehwirth-Schnatter
A1.01, Zeeman Building

Prof Sylvia Fruehwirth-Schnatter, Johannes Kepler University, Austria


Bayesian Variable Selection Problems for State Space and other Latent Variable Models

Latent Variable models are widely used in applied statistics and econometrics to deal with data where the underlying processes change either over time or between units.  Whereas estimation of these models is well understood, model selection problems are rarely studies, because such an issue usually leads to a non-regular testing problem.

Bayesian statistics offers in principle a framework for model selection even for non-regular problems, as is shortly discussed in the first part of the talk.  The practical application of the Bayesian approach, however, proves to be challenging and numerical technique like marginal likelihoods, RJMCMC or the variable selection approach have to be used.

The main contribution of this talk is to demonstrate that the Bayesian variable selection approach is useful far beyond the common problem of selecting covariates in a classical regression model and may be extended to deal model selection problems in various latent variable models.  First, it is extended to testing for the presence of unobserved heterogeneity in random effects models.  Second, dynamic regression models are considered, where one has to choose between fixed and random coefficients.  Finally, the variable selection approach is extended to state space models, where testing problems like discriminating between models with a stochastic trend, a deterministic trend and a model without trend arise.

Case studies from marketing, economics and finance will be considered for illustration.

 
14:30 - 15:30
CRiSM Seminar - John Cussens
A1.01, Zeeman Building

James Cussens, University of York

 Model Selection using weighted MAX-SAT Solvers

This talk concerns encoding problems of statistical model selection in such a way that "weighted MAX-SAT solvers" can be used to search for the   'best' model. In this approach each model is (implicitly) encoded as a joint instantiation of n binary variables. Each of these binary variables encodes the truth/falsity of a logical proposition and weighted logical formulae are used to represent the model selection problem. Once encoded in this way we can tap into years of research and use any of the state-of-the-art solvers to conduct the search. In the talk I will show how to use this approach when the model class is that of Bayesian networks, and also for clustering. I will briefly touch on related methods which permit the calculation of marginal probabilities in discrete distributions.

Thu, Nov 6, '08
16:00 - 17:00
CRiSM Seminar: Ming-Yen Cheng
A1.01

Prof Ming-Yen Cheng UCL
Generalized Multiparameter Likelihood Models
Multiparameter likelihood models (MLM) with multiple covariates have a wide range of applications. However, they encounter the ``curse of dimensionality" problem when the dimension of the covariates is large. We develop a generalized multiparameter likelihood model that copes with multiple covariates and adapts to dynamic structural changes well. And it includes some popular models, such as the partially linear and varying coefficient models, as special cases. When the model is fixed, a simple and effective two-step method is developed to estimate both the parametric and the nonparametric components.  The proposed estimator of the parametric component has the root-n convergence rate, and the estimator of the nonparametric component enjoys an adaptivity property. A data-driven procedure is suggested to select the bandwidths involved. Also proposed is a new initial estimator in profile likelihood estimation of the parametric part to ensure stability of the approach in general settings. We further develop an automatic procedure to identify constant parameters in the underlying model. A simulation study and an application to the  infant mortality data of China are given to demonstrate performance of the proposed methods.

Thu, Oct 30, '08
16:00 - 17:00
CRiSM Seminar: Christopher Sherlock
A1.01
Dr Christopher Sherlock
Optimal scaling of the random walk Metropolis
University of Lancaster
Abstract: The random walk Metropolis (RWM) is one of the most commonly used Metropolis-Hasting algorithms, and choosing the appropriate scaling for the proposal is an important practical problem. Previous theoretical approaches have focussed on high-dimensional algorithms and have revolved around a diffusion approximation of the trajectory. For certain specific classes of targets it has been possible to show that the algorithm is optimal when the acceptance rate is approximately
0.234.

We develop a novel approach which avoids the need for diffusion limits. Focussing on spherically symmetric targets, it is possible to derive simple exact formulae for efficiency and acceptance rate for a "real" RWM algorithm, as opposed to a limit process. The limiting behaviour of these formulae can then be explored. This in some sense "simpler" approach allows important general intuitions as to when and why the 0.234 rule holds, when the rule fails, and what may happen when it does fail. By extending the theory to include elliptically symmetric targets we obtain further intuitions about the role of the proposal's shape.
Thu, Oct 23, '08
14:15 - 17:00
Oxford-Warwick Joint Seminar
Oxford

 

3rd JOINT WARWICK-OXFORD STATISTICS SEMINAR

2:30 – 5:00 pm  at The Mary Ogilvie Lecture Theatre,

St. Anne’s College, University of Oxford

2:30 p.m.

Speaker 1:  Julian Besag (University of Bath, University of Washington, Seattle)

Title:  Continuum limits of Gaussian Markov random fields: resolving the conflict with geostatistics

Abstract:  For more than 30 years, Markov random fields (equivalently, graphical models with undirected edges) have been used with some success to account for spatial variation in data. Applications include agricultural crop trials, geographical epidemiology, medical imaging, remote sensing, astronomy, and microarrays. Almost all of the examples involve (hidden) Gaussian MRF formulations.

MRFs refer to fixed regular or irregular discrete lattices or arrays and questions arise regarding inconsistencies between MRFs specified at differing scales, especially for regional data. Ideally, one would often prefer an underlying continuum formulation, as in geostatistics, which can then be integrated to the regions of interest. However, limiting continuum versions of MRFs, as lattice spacing decreases, proved elusive until recently.

This talk briefly presents some motivating examples and shows that limiting processes indeed exist but are defined on arbitrary regions of the plane rather than pointwise. Especially common is the conformally invariant de Wijs process, which coincidentally was used originally by mining engineers but which became unfashionable as geostatistics developed. Convergence is generally very fast. The de Wijs process is also shown to be a natural extension of Brownian motion to the plane. Other processes, including the thin-plate spline, can be derived as limits of MRFs. The talk closes by briefly discussing data analysis.

 

ÍÎ

 

3:30 to 4.00 - Tea, Coffee and biscuits in foyer outside lecture theatre

 

4:00 p.m.

Speaker 2:   Susan Lewis (University of Southampton, UK)

Title:  Screening experiments

Abstract:  Discovery and development in science and industry often involves investigation of many features or factors that could potentially affect the performance of a product or process. In factor screening, designed experiments are used to identify efficiently the few features that influence key properties of the system under study. A brief overview of this broad area will be presented. This will be followed by discussion of a variety of methods with particular emphasis on industrial screening. Ideas will be motivated and illustrated through examples, including a case study from the automotive industry.

5:00 reception in the foyer
Thu, Oct 2, '08
16:00 - 17:00
CRiSM Seminar: Martin Baxter
A1.01
Dr Martin Baxter, Nomura International
Levy Modelling of Credit

This talk will start with some simple models of credit dynamics, and embed them in a general Levy process framework. A particular instance, the Gamma process, will then be studied with reference to both its theoretical and practical properties. A brief analysis of the ongoing credit crisis in terms of Levy modelling. Time permitting, we will also look at some other applications.

Mon, Sep 22, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Dr Jonathan Evans, Institute of Linguistics, Academia Sinica
Statistical Modelling in Linguistics: Approaches and Challenges in pitch analysis

This talk introduces the use of Linear Mixed Effects (LME) analysis to model f0 (pitch) production in a language with two  tones, and demonstrates the advantages of using such a method of analysis.  LME can be used to weigh the impact of a large number of effects, it can demonstrate the interaction among those effects, and can also show how both fixed and random effects contribute to the model.  Unlike previous analytical methods for modeling f0 in tone languages, LME analysis allows researchers to have more freedom in designing experiments, and to have sufficient variety in the dataset without having to rely on nonsense words and phrases to fill out a data matrix. LME makes it is possible to put a multitude of effects and interactions into a single comprehensive model of f0.  The ensuing model is easy to interpret and straightforward to compare crosslinguistically.  LME analysis makes possible a quantitative typology that shows clearly how linguistic and nonlinguistic factors combine in the production of f0 for each language thus analyzed. The talk will also veer into discussion of how to model f0 based on the pitch curve of each syllable.  Although each curve contains an infinite number of points, there is striking similarity between the curve-based model and the point-based model.

 
Tue, Sep 9, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Professor P Cheng, Academia Sinica, Taipei, Republic of China
Linear Information Models and Applications
Log-likelihood information identities and Venn diagrams for categorical data exhibit fundamental differences from those of continuous variables. This presentation will start with three-way contingency tables and the associated likelihood ratio tests. It will introduce linear information models that deviate from hierarchical log-linear models, beginning with three-way tables. A connection to latent class analysis with two-way tables and the geometry of the one-degree-freedom chi-square test and exact test for two-way independence is also investigated.

Key Names: Pearson; Fisher; Neyman and Pearson; Kullback and Leibler; Cochran, Mantel, and Heanszel; Goodman.

Co-authors: John A. D. Aston, Jiun W. Liou, and Michelle Liou.

Mon, Aug 25, '08
13:00 - 14:00
Economics/Stats Seminar
S2.79
Donald Rubin (Harvard)
For Objective Causal Inference, Design Trumps Analysis
For obtaining causal inference that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard.  Observational studies, in contrast, are generally fraught with problems that compromise any claim for objectivity of the resulting causal inferences.  The thesis here is that observational studies have to be carefully designed to approximate randomized experiments, in particular, without examining any final outcome data.  Often a candidate data set will have to be rejected as inadequate because of lack of data on key covariates, or because of lack of overlap in the distributions of key covariates between treatment and control groups, often revealed by careful propensity score analyses.  Sometimes the template for the approximating randomized experiment will have to be altered, and the use of principal stratification can be helpful in doing this.  These issues are discussed and illustrated using the framework of potential outcomes to define causal effects, which greatly clarifies critical issues.
Mon, Jul 14, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Prof Donald Martin, North Carolina State University
Markov chain pattern distributions
We give a method for predicting statistics of hidden state sequences, where the conditional distribution of states given observations is modeled by a factor graph with factors that depend on past states but not future ones.  Model structure is exploited to develop a deterministic finite automaton and an associated Markov chain that facilitates efficient computation of the distributions.  Examples of applications of the methodology are the computation of distributions of patterns and statistics in a discrete hidden state sequence perturbed by noise and/or missing values, and patterns in a state sequence that serves to classify the observations.  Two detailed examples are given to illustrate the computational procedure. 
Thu, Jun 26, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Gersende Fort, ENST (Ecole Nationale Superieure Des Telecommunications, France
Stability of Markov Chains based on fluid limit techniques. Applications to MCMC
We propose a transformation of some Markov chains which will allow us to define its fluid limit: by renormalization in time, space, and initial value of the chain, we exhibit a time-continuous process which governs the dynamic of the initial chain. The goal is to identify the quantities that govern the ergodic behavior of the Markov chain, by showing their impact on the dynamics of the associated fluid  process which, by definition, gives information on  the transient steps of the chain. We will consider  applications of these techniques to the choice of the design parameters of some MCMC samplers.
Thu, Jun 19, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Ian Dryden, University of Nottingham
Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging or longitudinal data analysis. Methodology is discussed for estimating covariance matrices which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. We make connections with the use of Procrustes methods in shape analysis, and comparisons are made with other estimation techniques, including using the matrix logarithm, Riemannian metric, matrix square root and Cholesky decomposition. Our main application will be diffusion tensor imaging which is used to study the fibre structure in the white matter of the brain. Diffusion weighted MR images involve applying a set of gradients in a design of directions, and the recorded data are related to the Fourier transforms of the displacement of water molecules at each voxel. Under a multivariate Gaussian diffusion model a single tensor (3 x 3 covariance matrix) is fitted at each voxel. We discuss the statistical analysis of diffusion tensors, including construction of means, spatial interpolation, geoedsics, and principal components analysis. This is joint work with Alexey Koloydenko and Diwei Zhou.

Thu, Jun 12, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Jonathan Dark, University of Melbourne
Dynamic hedging with futures that are subject to price limits
The standard approaches to estimating minimum variance hedge ratios (MVHRs) are mis-specified when futures prices are subject to price limits. This paper proposes a bivariate tobit-FIGARCH model with maturity effects to estimate dynamic MVHRs using single and multiple period approaches. Simulations and an application to a commodity futures hedge support the proposed approach and highlight the importance of allowing for price limits when hedging.   
Thu, Jun 5, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Thomas Nichols, GlaxoSmithKline Clinical Imaging Centre
Cluster mass inference - a new random field theory method for neuroimaging
Functional and structural brain imaging analyses typically fit univariate models at each volume element, or voxel, producing images of T-statistics. These statistics images must be threshold or assessed insome way to identify significant regions while controlling some specified false positive rate. A widely used method for assessing signficance is the cluster size test, where an arbitary threshold is applied to the statistic image and contiguous suprathreshold voxels are grouped into clusters. The size of a cluster forms a test statistic on the null hypothesis of no activation anywhere within the cluster, and P-values are found with Random Field Theory (RFT). Various authors have reported on improved sensitivity with a modified version of the cluster size test, the cluster mass test. Cluster mass is the integral of suprathreshold intensities within the cluster, and captures information about both the extent and magnitude of the effect. However, all previous work has relied on permutation inference as no distributional results have been available. I will show recent work on deriving a null distribution for cluster mass using RFT. Using the approximate parabolic shape about local maxima and distributional results for the cluster extent and peak curvature, we produce a joint distribution for mass and peak height which is marginalized to produce a P-value for the mass statistic. We show results on simulated and real data which demonstrate the tests validity and power. 

Thu, May 29, '08
15:00 - 16:00
CRiSM Seminar
A1.01

Geoff McLachlan, University of Queensland
On Simple Mixture Models in High-Dimensional Testing in the Detection of Differentially Expressed Genes

An important problem in microarray experiments is the detection of genes that are differentially expresse in a given number of classes. As there are usually thousands of genes to be considered simultaneously, one encounters high-dimensional testing problems. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null (not differentially expressed).  The problem can be expressed in a two-component mixture framework.  Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with the computationally intensive nature of more specific assumptions. By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The approach provides an estimate of the local false discovery rate (FDR) for each gene, which is taken to be the posterior probability that the gene is null.  Genes with the local FDR less than a specified threshold C are taken to be differentially expressed.  For a given C, this approach also provides estimates of the implied overall errors such as the (global) FDR and the false negative/positive rates.

Thu, May 22, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Thomas Richardson, University of Washington
Estimation of the Relative Risk and Risk Difference

I will first review well-known differences between odds ratios, relative risks and risk differences. These results motivate the development of methods, analogous to logistic regression, for estimating the latter two quantities. I will then describe simple parametrizations that facilitate maximum-likelihood estimation of the relative risk and risk-difference. Further, these parametrizations allow for doubly-robust g-estimation of the relative risk and risk difference. (Joint work with James Robins, Harvard School of Public Health).

Thu, May 8, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Cees Diks, University of Amsterdam
Linear and Nonlinear Causal Relations in Exchange Rates and Oil Spot and Futures Prices
Various tests have been proposed recently in the literature for detecting causal relationships between time series. I will briefly review the traditional linear methods and some more recent contributions on testing for nonlinear Granger causality. The relative benefits and limitations of these methods are then compared in two different case studies with real data. In the first case study causal relations between six main currency exchange rates are considered. After correcting for linear causal dependence using VAR models there is still evidence presence for nonlinear causal relations between these currencies. ARCH and GARCH effects are insufficient to fully account for the nonlinear causality found. The second case study focuses on nonlinear causal linkages between daily spot and futures prices at different maturities of West Texas Intermediate crude oil. The results indicate that after correcting for possible cointegration, linear dependence and multivariate GARCH effects, some causal relations are still statistically significant. In both case studies the conclusion is that non-standard models need to be developed to fully capture the higher-order nonlinear dependence in the data.
Thu, May 1, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Alastair Young, Imperial College London
Objective Bayes and Conditional Inference
In Bayesian parametric inference, in the absence of subjective prior information about the parameter of interest, it is natural to consider use of an objective prior which leads to posterior probability quantiles which have, at least to some higher order approximation in terms of the sample size, the correct frequentist interpretation. Such priors are termed probability matching priors. In many circumstances, however, the appropriate frequentist inference is a conditional one. The key contexts involve inference in multi-parameter exponential families, where conditioning eliminates the nuisance parameter, and models which admit ancillary statistics, where conditioning on the ancillary is indicated by the conditionality principle of inference. In this talk, we consider conditions on the prior under which posterior quantiles have, to high order, the correct conditional frequentist interpretation. The key motivation for the work is that the conceptually simple objective Bayes route may provide accurate approximation to more complicated frequentist procedures. We focus on the exponential family context, where it turns out that the condition for higher order conditional frequentist accuracy reduces to a condition on the model, not the prior: when the condition is satisfied, as it is in many key situations, any first order probability matching prior (in the unconditional sense) automatically yields higher order conditional probability matching. We provide numerical illustrations, discuss the relationship between the objective Bayes inference and the parametric bootstrap, as well as giving a brief account appropriate to the ancillary statistic context, where conditional frequentist probability matching is more difficult. [This is joint work with Tom DiCiccio, Cornell].

Thu, Apr 3, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Professor Jay Kadane, Carnegie Mellon University
Driving While Black: Statisticians Measure Discriminatory Law Enforcement (joint work with John Lamberth)
The US Constitution guarantees "equal protection under the law" regardless of race, but sometimes law enforcement practices have failed to adhere to this standard.In the 1990's, a suit was brought alleging that the New Jersey State Police were stopping Blacks at disproportionately high rates in the southern end of the New Jersey Turnpike. In this talk I
* review the evidence in that case, the decision, and its immediate aftermath
* discuss criticisms of that decision
* examine new evidence that rebuts those criticisms
* comment on the extent to which the Constitutional standard is now being met.
Thu, Mar 13, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Prof Antony Pettitt, Lancaster University
Statistical inference for assessing infection control measures for the transmission of pathogens in hospitals
Patients can acquire infections from pathogen sources within hospitals and certain pathogens appear to be found mainly in hospitals.  Methicillin-resistant Staphylococcus Aureus (MRSA) is an example of a hospital acquired pathogen that continues to be of particular concern to patients and hospital management.  Patients infected with MRSA can develop severe infections which lead to increased patient morbidity and costs for the hospital.  Pathogen transmission to a patient can occur via health-care workers that do not regularly perform hand hygiene.  Infection control measures that can be considered include isolation for colonised patients and improved hand hygiene for health-care workers.

The talk develops statistical methods and models in order to assess the effectiveness of the two control measures (i) isolation and (ii) improved hand hygiene.  For isolation, data from a prospective study carried out in a London hospital is considered and statistical models based on detailed patient data are used to determine the effectiveness of isolation.  The approach is Bayesian.
For hand hygiene it is not possible, for ethical and practical reasons, to carry out a prospective study to investigate various levels of hand hygiene.  Instead hand hygiene effects are investigated by simulation using parameter values estimated from data on health-care worker hand hygiene and weekly colonisation incidence collected from a hospital ward in Brisbane.  The approach uses profile likelihoods.Both approaches involve transmission parameters where there is little information available and contrasting compromises have to be made. Conclusions about the effectiveness of the two infection control measures will be discussed. The talk involves collaborative work with Marie Forrester, Emma McBryde, Chris Drovandi, Ben Cooper, Gavin Gibson, Sean McElwain.

 

Thu, Mar 6, '08
16:00 - 17:00
CRiSM Seminar
A1.01
Dr Cliona Golden, UCD, Dublin
On the validity of ICA for fMRI data
Functional Magnetic Resonance Imaging (fMRI) is a brain-imaging technique which, over time, records changes in blood oxygenation level that can be associated with underlying neural activity. However, fMRI images are very noisy and extracting useful information from them calls for a variety of methods of analysis.

I will discuss the validity of the use of two popular Independent Component Analysis (ICA) algorithms, InfoMax and FastICA, which are commonly used for fMRI data analysis.

Tests of the two algorithms on simulated, as well as real, fMRI data, suggest that their successes are related to their ability to detect "sparsity" rather than the independence which ICA is designed to seek.
Thu, Feb 28, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Alexey Koloydenko & Juri Lember (Joint Talk), University of Nottingham
Adjusted Viterbi Training for Hidden Markov Models
The Expectation Maximisation (EM) procedure is a principal tool for parameter estimation in hidden Markov models (HMMs). However, in applications EM is sometimes replaced by Viterbi training, or extraction, (VT). VT is computationally less intensive and more stable, and has more of an intuitive appeal, but VT estimation is biased and does not satisfy the following fixed point property: Hypothetically, given an infinitely large sample and initialized to the true parameters, VT will generally move away from the initial values. We propose adjusted Viterbi training (VA), a new method to restore the fixed point property and thus alleviate the overall imprecision of the VT estimators, while preserving the computational advantages of the baseline VT algorithm. Simulations show that VA indeed improves estimation precision appreciably in both the special case of mixture models and more general HMMs.

We will discuss the main idea of the adjusted Viterbi training. This will also touch on tools developed specifically to analyze asymptotic behaviour of maximum a posteriori (MAP) hidden paths, also known as Viterbi alignments. Our VA correction is analytic and relies on infinite Viterbi alignments and associated limiting probability distributions. While explicit in the special case of mixture models, these limiting measures are not obvious to exist for more general HMMs. We will conclude by presenting a result that under certain mild conditions, general (discrete time) HMMs do possess the limiting distributions required for the construction of VA. 

Mon, Feb 18, '08
15:00 - 16:00
CRiSM Seminar
A1.01

Terry Speed, University of California, Berkeley
Alternative Splicing in Tumors: Detection and Interpretation
In this talk I will discuss using the Affymetrix GeneChip Human Exon and Human Gene 1.0 ST arrays for the detection of genes spliced differently in some tumors in comparison with others. I plan to begin by introducing the arrays and the expression data they produce. Next I will outline the way in which we use such data in our attempts to identify exon-tumor combinations exhibiting splicing patterns different from the majority. This will be illustrated by examples from publicly available tissue and mixture data. Then I will briefly discuss some of the additional issues which arise when we seek to enumerate such alternative splicing patterns on a genome-wide scale. Finally, I will exhibit some of the results we have found applying these methods to glioblastoma tissue samples collected as part of The Cancer Genome Atlas (TCGA) project. (This is joint work with ELizabeth Purdom, Mark Robinson, Ken Simpson, and members of the Berkeley Cancer Genome Center.)

Thu, Feb 14, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Professor Simon Wood, University of Bath
Generalized Additive Smooth Modelling
Generalized Additive Models are GLMs in which the linear predictor is made up, partly, of a sum of smooth functions of predictor variables. I will talk about the penalized regression spline approach to GAM, as implemented, for example, in R package mgcv. In particular I will focus on two interesting aspects: low rank representation of smooth functions of several covariates and stable computation of both model coefficients and smoothing parameters. More than half the slides will have pictures.
 

Thu, Jan 31, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Dr Robert Gramacy, Statistical Laboratory Cambridge
Importance Tempering
Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density pi(theta).  The technique involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say pi_k(theta) = pi(theta)^k.  Small values of k encourage better mixing, but samples from pi are only obtained when the joint chain for (theta,k) reaches k=1. However, the entire chain can be used to estimate expectations under pi of functions of interest, provided that importance sampling (IS) weights are calculated.  Unfortunately this method, which we call importance tempering (IT),  has tended not work well in practice.  This is partly because the most immediately obvious implementation is naive and can lead to high variance estimators.  We derive a new optimal method for combining multiple IS estimators and prove that this optimal combination has a highly desirable property related to the notion of effective sample size.  The methodology is applied in two modelling scenarios requiring reversible-jump MCMC, where the naive approach to IT fails: model averaging in treed models, and model selection for mark--recapture data. 

Thu, Jan 24, '08
16:00 - 17:00
CRiSM Seminar
A1.01

Dr Richard Samworth, Statistical Laboratory, Cambridge
Computing the maximum likelihood estimator of a multidimensional log-concave density

We show that if $X_1,...,X_n$ are a random sample from a log-concave density $f$ in $\mathbb{R}^d$, then with probability one there exists a unique maximum likelihood estimator $\hat{f}_n$ of $f$.  The use of this estimator is attractive because, unlike kernel density estimation, the estimator is fully automatic, with no smoothing parameters to choose. The existence proof is non-constructive, however, and in practice we require an iterative algorithm that converges to the estimator.  By reformulating the problem as one of non-differentiable convex optimisation, we are able to exhibit such an algorithm.  We will also show how the method can be combined with the EM algorithm to fit finite mixtures of log-concave densities.  The talk will be illustrated with pictures from the R package LogConcDEAD.

This is joint work with Madeleine Cule (Cambridge), Bobby Gramacy (Cambridge) and Michael Stewart (University of Sydney).

Thu, Jan 17, '08
16:00 - 17:00
CRiSM Seminar

Dr Elena Kulinskaya, Statistical Advisory Service, Imperial College
Meta analysis on the right scale

This talk is about an approach to meta analysis and to statistical evidence developed jointly with Stephan Morgenthaler and Robert Staudte, and now written up in our book 'Meta Analysis: a guide to calibrating and combining statistical evidence'  to be published by Wiley very soon. The traditional ways of measuring evidence, in particular with p-values, are neither intuitive nor useful when it comes to making comparisons between experimental results, or when combining them. We measure evidence for an alternative hypothesis, not evidence against a null. To do this, we have in a sense adopted standardized scores for the calibration scale. Evidence for us is simply a transformation of a test statistic S to another one (called evidence T=T(S)) whose distribution is close to normal with variance 1, and whose mean grows from 0 with the parameter as it moves away from the null. Variance stabilization is used to arrive on this scale. For meta analysis the results from different studies are transformed to a common calibration scale, where it is simpler to combine and interpret them. 

Thu, Dec 13, '07
16:00 - 17:00
CRiSM Seminar
A1.01

Professor Malcolm Faddy, Queensland University of Technology, Australia
Analysing hospital length of stay data: models that fit, models that don’t and does it matter?

Hospital length of stay data typically show a distribution with a mode near zero and a long right tail, and can be hard to model adequately. Traditional models include the gamma and log-normal distributions, both with a quadratic variance-mean relationship. Phase-type distributions which describe the length of time to absorption of a Markov chain with a single absorbing state also have a quadratic variance-mean relationship. Covariates of interest include an estimate of the length of stay for an uncomplicated admission, with excess length of stay modelled relative to this quantity either multiplicatively or additively. A number of different models can therefore be constructed, and the results of fitting these models will be discussed in terms of goodness of fit, significance of covariate effects and estimation of quantities of interest to health economists.

Thu, Nov 29, '07
16:00 - 18:00
CRiSM Seminar
A1.01

Dr Sumeet Singh, Signal Processing Laboratory, Cambridge
Filters for spatial point processes

We consider the inference of a hidden spatial Point Process (PP) X on a CSMS (complete separable metric space) X, from a noisy observation y modeled as the realisation of another spatial PP Y on a CSMS Y. We consider a general model for the observed process Y which includes thinning and displacement and characterise the posterior distribution of X for a Poisson and Gauss-Poisson prior.  These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of X considered are general enough for many arget Tracking applications,  which is an important study area in Engineering. Accompanying numerical implementations based on Sequential Monte Carlo will be presented.

Thu, Nov 22, '07
16:00 - 17:00
CRiSM Seminar
A1.01

Prof Gareth Roberts, University of Warwick (Joint Statistics/Econometrics Seminar)
This presentation will review recent work in the area of Bayesian inference for discretely (and partially) observed diffusion. I will concentrate on Bayesian approaches which necessitate the use of Markov chain Monte Carlo techniques, and the talk will consider the problem of MCMC algorithm design. The approach will be presented in a continuous-time framework.

Thu, Nov 15, '07
16:00 - 18:00
CRiSM Seminar
A1.01

Dr Daniel Farewell, Cardiff University
Simple models for informatively censored longitudinal data

Models for longitudinal measurements truncated by possibly informative dropout have tended to be either mathematically complex or computationally demanding. I will review an alternative recently proposed in our RSS discussion paper (Diggle et al. 2007), using simple ideas from event-history analysis (where censoring is commonplace) to yield moment-based estimators for balanced, continuous longitudinal data. I shall then discuss  some work in progress: extending these ideas to more general longitudinal data, while maintaining simplicity of understanding and implementation.

Thu, Nov 1, '07
16:00 - 18:00
CRiSM Seminar
A1.01

Prof Valentine Genon-Catalot, Paris 5
Explicit filtering of discretized diffusions

Consider a pair signal-observation ((x_n, y_n), n > 0) where the unobserved signal (x_n) is a Markov chain and the observed component is such that, given the whole sequence (x_n), the random variables (y_n) are independent and the conditional distribution of y_n only depends on the corresponding state variable x_n.  Concrete problems raised by these observations are the prediction, filtering or smoothing of (x_n).  This requires the computation of the conditional distributions of x_l given y_n, . . . , y_1, y_0 for all l, n.  We introduce sufficient conditions allowing to obtain explicit formulae for these conditional distributions and extend the notion of finite dimensional filters using mixtures of distributions.  The method is applied to the case where the signal x_n = Xn_ is a discrete sampling of a one dimensional diffusion process: Concrete models are proved to fit in our conditions.  Moreover, for these models, exact likelihood inference based on the observation (y_0, . . . , y_n) is feasible.

 

Wed, Oct 31, '07
16:00 - 18:00
CRiSM Seminar
A1.01

Dr Alex Schmidt, Instituto de Matematica - UFRJ, Brazil
Modelling multiple series of runoff:  The case of Rio Grande Basin (joint work with Romy R Ravines and Helio S Migon)

This paper proposes a joint model for the rainfall and multiple series of runoff at a basin, two of the most important hydrological processes.  The proposed model takes into account the different spatial units in which these variables are measured, and as a natural benefit its parameters have physical interpretations. Also, we propose to model runoff and rainfall in their original scales, making no use of any transformation to reach normality of the data. More specifically, our proposal follows Bayesian dynamic nonlinear models through the use of transfer function models.  The resultant posterior distribution has no analytical solution and stochastic simulation methods are needed to obtain samples from the target istribution.  In particular, as the parameters of the dynamic model are highly correlated, we make use of the Conjugate Updating Backward Sampling recently proposed by Ravines, Migon and Schmidt (2007), in order to efficiently explore the space of the parameters. We analyze a sample from a basin located in the Northeast of Brazil, the Rio Grande Basin. The data consist of monthly recorded series from January 1984 to September 2004, at three runoff stations and nine rainfall monitoring stations, irregularly located in an area of drainage of 37,500 sq km. Model assessment, spatial interpolation and temporal predictions are part of our analysis. Results show that our approach is a promising tool for the runoff-rainfall analysis.

Thu, Oct 25, '07
16:00 - 17:00
CRiSM Seminar
A1.01

Prof Wilfrid Kendall, University of Warwick
Short-length routes in low-cost networks via Poisson line patterns (joint work with David Aldous)

How efficiently can one move about in a network linking a configuration of n cities? Here the notion of "efficient" has to balance (a) total network length against (b) short network distances between cities. My talk will explain how to use Poisson line processes to produce networks which are nearly of shortest total length, which make the average inter-city distance almost Euclidean.

Thu, Oct 11, '07
15:00 - 18:00
CRiSM seminar

OXFORD-WARWICK JOINT SEMINAR

Prof Odd Aalen, Dept of Biostatistics, University of Oslo (3-4pm Rm L4, Science Concourse Main Level)
Statistics, causality and dynamic path modelling

Prof Geert Molenberghs, Centre for Statistics, Hasselt University, Belgium (4.30-5.30 Rm LIB1, Library)
Model assessment and sensitivity analysis when data are incomplete

Abstracts

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