Bayesian Variable Selection in Regression with Networked Predictors

Abstract

We consider Bayesian variable selection in linear regression when the relationships among a possibly large number of predictors are described by a network given a priori. A class of motivating examples is to predict some clinical outcomes with high-dimensional gene expression profiles and a gene network, for which it is assumed that the genes neighboring to each other in the network are more likely to participate together in relevant biological processes and thus more likely to be simultaneously included in (or excluded from) the regression model. To account for spatial correlations induced by a predictor network, rather than using an independent (and identical) prior distribution for each predictor’s being included in the model as implemented in the standard approach of stochastic search variable selection (SSVS), we propose a Gaussian Markov random field (MRF) and a binary MRF as priors. We evaluate and compare the performance of the new methods against the standard SSVS using both simulated and real data.