Semiparametric Bayes Graphical Models Incorporating Covariates with Applications to Imaging Genetics

• Activity Number: 26
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Suprateek Kundu* and Jian Kang
• Companies: Emory University and Emory University
• Keywords: Semi-parametric Bayes ; Graphical Models ; Variable selection ; Brain Networks ; Imaging Genetics

Abstract

There have been significant advances separately in estimation of graphical models and variable selection, however sparse attention has been paid to high-dimensional joint covariance and covariate selection. We propose a semi-parametric Bayesian regression model for multivariate outcomes involving a linear mean, which engages in dimension reduction by clustering the columns of the coefficient matrix under an infinite mixture of Laplace distributions. The associations between the outcomes are characterized by a novel class of semi-parametric graphical priors which assumes independence between outcomes belonging to distinct clusters given covariate information, thereby inducing sparsity in the precision matrix via a block diagonal formulation. The posterior computation proceeds using a parameter expansion strategy, and is designed to efficiently explore the graph space via multiple edges-at-a-time moves involving negligible additional burden and which can be parallelized. Our methods are motivated by imaging genetics applications, where the objective is to infer genetic influences on brain functional connectivity. We demonstrate the advantages of our approach via a simulation study.