The Posterior Predictive Information Criterion

• Activity Number: 586
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Andrew Womack*+
• Companies: Washington University in St. Louis
• Keywords: posterior predictive density ; information criterion ; model selection

Abstract

This paper introduces a new information theoretic model selection criterion based on Bayesian posterior predictive densities that resolves criticisms of other methods, including: necessity of asymptotics, choice of model focus, data splitting, and asymmetry in the treatment of models. The criterion is a Kullback-Leibler correction to the Posterior Bayes Factor that corrects for over-fitting. Inherent in the method is a Bayesian power calculation, thus it naturally balances Type I and Type II error. As it is based on posterior predictive densities, this criterion also allows for the use of improper priors without suffering from the indeterminacy of such priors. Properties of the criterion are shown and key examples are used to exhibit consistency and draw direct comparisons between this method and popular criteria.