July 2005

Zellner's g-prior remains a popular conventional prior for use in Bayesian variable selection, despite several well known consistency problems.  In this paper, we study mixtures of g-priors as an alternative to default g-priors that resolve many of the problems with the original  formulation, while maintaining the computational tractability that has made the g prior so popular. We present theoretical properties of the mixture priors and provide real and simulated examples to compare the mixture formulation with fixed g-priors, Empirical Bayes approaches and other default procedures.