Calibrated Bayes Factors for Model Comparison

• Activity Number: 147
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xinyi Xu*+ and Pingbo Lu and Steven MacEachern and Ruoxi Xu
• Companies: The Ohio State University and The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Prior elicitation ; Training sample ; Predictive performance ; Information level ; Unit information prior

Abstract

Bayes factor is a widely used tool for Bayesian hypothesis testing and model comparison. However, it can be greatly affected by the prior elicitation for the model parameters. When the prior information is weak, people often use proper priors with large variances. In this work, we show that Bayes factors under convenient diffuse priors can be misleading when the models under comparisons differ in dimensions. Therefore, we propose an innovative method called calibrated Bayes factor, which uses data to calibrate the prior distributions before computing Bayes factors. We show that this method provides reliable and robust model preferences under various true models. It makes no assumption on model forms (parametric or nonparametric) or on the integrability of priors (proper or improper), so is applicable in a large variety of model comparison problems.