Robust Bayesian Variable Selection and Its Application to QTL Studies

• Activity Number: 89
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Cheongeun Oh*+
• Companies: Yale University
• Keywords: Bayesian ; variable selection ; QTL problems

Abstract

Variable selection is a crucial problem in multiple regression. From a Bayesian prospective, George and McCulloch (1993) proposed a procedure that uses Gibbs sampling for selection promising subsets, called Stochastic Search Variable Selection. It entails embedding a hierarchical normal mixture model in the regression setup where latent variables are used to identify subset choices. However, as pointed by several authors, results of their procedure are highly sensitive to priors. The purpose of this paper is to develop a robust and efficient Bayesian variable selection method. We propose two important modifications. First, we modify a prior structure on the coefficients to make the procedure computationally efficient, especially when a large number of candidate factors are considered. Second, instead of looking at the posterior distribution of each candidate model, we focus ranking the candidate variables according to their marginal posterior probability, which is shown to be more robust. We also suggest how to deal with highly correlated factors which have been known as a major challenge for Stochastic Search Variable Selection.