Bayesian Models for Sparse Regression Analysis of High Dimensional Data

This talk considers the task of building efficient regression models for sparse multivariate analysis of high dimensional data sets, in particular it focuses on cases where the numbers q of responses and p of predictors to analyze jointly are both large with respect to the sample size n, a challenging bi-directional task. The analysis of such data sets arise commonly in genetical genomics, with the design matrix linked to the DNA characteristics and the multiple responses corresponding to measurements of fundamental biological processes such as transcription, protein or metabolite production.
To perform Bayesian inference for these models in high dimensional set-ups, novel adaptive MCMC algorithms are needed. We shall discuss their formulation and theoretical properties, and demonstrate their use on simulated and real data from genomics. This is a joint work with Sylvia Richardson (ICL), Krzysztof Latuszynski (Warwick) and Jeff Rosenthal (Toronto