Criteria for Bayesian model choice with application to variable selection

Abstract

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.

Published in at http://dx.doi.org/10.1214/12-AOS1013 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Fully Bayes factors with a generalized g-prior
• Consistency of Bayesian procedures for variable selection
• Harold Jeffreys's Theory of Probability Revisited
• Robust Bayesian variable selection with sub-harmonic priors

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