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Warwick Oxford Joint Seminar (at Warwick)

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Location: 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.]

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Tags: CRiSM Seminars Seminars

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