Bayesian Modeling with Blockwise Hyper-G Priors

• Activity Number: 221
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Agniva Som*+ and Christopher Hans and Steven N. MacEachern
• Companies: Ohio State University and Ohio State University and Ohio State University
• Keywords: g prior ; conditional Lindley's paradox ; information paradox ; model selection ; consistency ; Gaussian hypergeometric function

Abstract

Availability of closed form analytic representations of the Bayes factors under Zellner's g prior and its amelioration in the form of the mixtures of g priors helps to downscale the computational burden of inference in large problems and is a major reason for the widespread use of such priors. The hyper-g prior was formulated to address critical inconsistency issues associated with the original (fixed) g prior. Our investigations show that in spite of effectively dealing with the well-known paradoxes, the hyper-g prior still suffers from an alternative paradox when non-zero regression coefficients differ greatly in magnitude and basically collapses to a least squares solution in certain situations. In this article, we modify the ordinary g prior by proposing independent g priors on groups (or blocks) of predictor variables and investigate the theoretical properties of the new prior under a blockwise orthogonal design. We show that mixtures of blockwise g priors with carefully chosen blocks are capable of fixing the troubling irregularities associated with their g prior counterparts and also exhibit all the desirable properties of a sound modeling procedure.