The Role of Efron's Statistical Curvature in Bayesian Model Selection

• Activity Number: 259
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Cedric E. Ginestet*+
• Companies: Imperial College London
• Keywords: information geometry ; statistical curvature ; model selection ; Bayes information criterion ; Fisher information matrix ; Riemannian volume

Abstract

Information geometry has received a wide amount of interest in statistics, particularly regarding model estimation and the theory of tests. This article generalizes some of the findings in information geometry to a Bayesian setting. In particular, we show that the Efron's curvature of a statistical model is a monotonic decreasing function of the information metric. This finding enables us to shed light on some counterintuitive expansions of the integrated likelihood. These results indicate that the optimal model under the Bayes rule, is the one, which optimizes the inverse of the Fisher information at the maximum likelihood (MLE). We give a geometrical explanation of this fact, by linking the information metric with the volume element of a statistical manifold, and therefore showing that the smallest information at the MLE is indeed desirable to ensure parsimony.