Predictive Bayes Factor

• Activity Number: 22
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Shouhao Zhou*+
• Companies: Columbia University
• Keywords: Bayesian model comparison ; Bayes factor ; predictive Bayes factor ; posterior predictive distribution ; Kullback-Leibler divergence ; posterior predictive information criterion

Abstract

In this article we investigate and develop the practical model assessment and selection methods for Bayesian models. By re-visiting the philosophy underneath the Bayes factors after taking a close look at the candidate Bayesian models for pairwise comparison, we find that the standard Bayes factor and its derivatives compare the proposed original models, other than the fitted models of general interest for Bayesian researchers. Taking the above into account, we propose the predictive Bayes factor (PrBF) to compare the fitted model probabilities from a predictive perspective. In principle, PrBF is introduced on top of the posterior predictive information criterion (PPIC), a versatile asymptotic method which unbiasedly estimates the ad hoc Kullback-Leibler discrepancy, when each candidate model is evaluated through the posterior predictive distribution of a future observation. For illustrative purpose, we perform the numerical comparison of the predictive Bayes factor with the standard Bayes factor to emphasize the empirical difference.