The Intrinsic Prior as a Scaled Mixture of G-Priors

• Activity Number: 622
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Andrew Womack*+
• Keywords: Linear Model ; Bayes Factors ; g-prior ; Bayesian Model Averaging ; Model Selection

Abstract

The use of objective Bayesian methods relies on the determination of automatic priors that provide both good posterior distributions and well behaving model selectors through Bayes Factors. The intrinsic prior has been shown by Casella, et. al. (2009) to provide a consistent selector in the class of linear models. In this paper we further this work by establishing that the intrinsic prior for the linear model is a scaled mixture of g-priors. The mixing distribution for g induced by the intrinsic prior depends on the sample sizes of both the observed and imaginary training data. Though the distribution of g depends on the encompassing model under consideration, an appropriate change of variables produces a prior which is independent of the encompassing model. Using this parameterization, efficient samplers can be built both for a single model and for the space of models, facilitating model selection and inference under model uncertainty. We further show that in the framework of Liang, et. al. (2008) the intrinsic prior resolves the so called "information paradox."