Mixtures of g priors for Bayesian variable selection

Zellner's g prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this article 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 g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors, empirical Bayes approaches, and other default procedures.