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Activity Number: 182
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #319137 View Presentation
Title: A Unified Framework for Bayes Factor Asymptotics
Author(s): Todd Kuffner* and Siddhartha Chib
Companies: Washington University in St. Louis and Washington University in St. Louis
Keywords: Asymptotics ; Bayes factor ; consistency ; model selection ; nonparametric ; semiparametric

Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool. As there exists such a wide variety of settings to be considered, e.g. parametric vs. nonparametric, nested vs. non-nested, etc., we adopt the view that a unified framework has didactic value. Using the basic marginal likelihood identity Chib (1995}, we propose a general framework for studying Bayes factor asymptotics, and demonstrate its utility for proving consistency in a wide variety of settings. A distinct feature of this approach is that it decomposes the marginal likelihood into three components, facilitating a more informative analysis of the asymptotic behavior of Bayes factors. This yields a convenient interpretation of the log ratio of posteriors as a penalty term, and emphasizes that to understand Bayes factor consistency, the prior support conditions driving posterior consistency in each respective model under comparison should be contrasted in terms of the rates of posterior contraction they imply.

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