Peter Muller
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.

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.

Siem Jan Koopman (Free University Amsterdam)

 

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.