Mixtures of <i>g</i> Priors for Bayesian Variable Selection

TLDR

Zellner's g prior remains a popular conventional prior for Bayesian variable selection, despite several undesirable consistency issues. This article studies mixtures of g priors as an alternative to default g priors that resolve many of the original formulation’s problems while preserving computational tractability. The authors present theoretical properties of the mixture g priors and illustrate them with real and simulated examples comparing the mixture formulation to fixed g priors, empirical Bayes approaches, and other default procedures. The mixture g priors demonstrate desirable theoretical properties and outperform fixed g priors, empirical Bayes, and other default procedures in both real and simulated analyses. Key terms include AIC, Bayesian model averaging, BIC, Cauchy, Empirical Bayes, Gaussian hypergeometric functions, model selection, and Zellner–Siow priors; see Zellner's letter and the author's response.

Abstract

AbstractZellner'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. Please see Arnold Zellner's letter and the author's response. KEY WORDS: AICBayesian model averagingBICCauchyEmpirical BayesGaussian hypergeometric functionsModel selectionZellner–Siow priors