Calibrated Bayes Factor for Model Comparison and Prediction

• Activity Number: 327
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xinyi Xu*+ and Steven MacEachern and Pingbo Lu and Ruoxi Xu
• Companies: The Ohio State University and The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Calibrated Bayes factor ; Cross validation ; Model comparison ; Training sample

Abstract

Bayes factor is a widely used tool for Bayesian hypothesis testing and model comparison. However, people have noticed that for the same pair of models under the same priors, Bayes factor can provide totally different model preferences when the sample size varies. In this work, we investigate this interesting phenomenon and develop a new calibrated Bayes factor, which is robust to sample size choices and consistently favors the model with better predictive performances. We show that the calibrated Bayes factor is an averaged partial Bayes factor, and we select the training sample size through a cross-validation approach.