Robust Bayesian Variable Selection with Sub-Harmonic Priors

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yuzo Maruyama*+
• Keywords: Bayes factor ; variable selection ; model selection consistency ; sub-harmonic prior

Abstract

This paper studies Bayesian variable selection in linear models with general spherically symmetric error distributions. We propose sub-harmonic priors which arise as a class of mixtures of Zellner's g-priors for which the Bayes factors are independent of the underlying error distribution, as long as it is spherically symmetric. Because of this invariance to spherically symmetric error distribution, we refer to our method as a robust Bayesian variable selection method. We demonstrate that our Bayes factors have model selection consistency and are coherent. We also develop Laplace approximations to Bayes factors for a number of recently studied mixtures of g-priors that have appeared in the literature (including our own) for Gaussian errors. These approximations, in each case, are given by the Gaussian Bayes factor based on BIC times a simple rational function of the prior's hyper-parameters and the R^2's for the respective models. We also extend model selection consistency for several g-prior based Bayes factor methods for Gaussian errors to the entire class of spherically symmetric error distributions. This is a joint work with Prof. William Strawderman (Rutgers U).