Systematic deviation in mean of log bayes factor: Implication and application

Abstract

This article works with an expression of the mean of log Bayes Factor to elucidate its dependence on specified priors. Such explication answers some basic questions about interpreting Bayes Factor as evidence against a null or an alternative hypothesis. It also provides a powerful tool to study the behavior of the Bayes Factor under various underlying distributions that may generate the data. A new concept, the neutral distribution, is proposed to evaluate performances of Bayesian methods across sample space. It quantifies the deviation in a log Bayes Factor in favoring the null hypothesis when the data is generated under an alternative hypothesis. Eventually this method provides a tool to obtain an estimate of the sample size needed to stand a reasonable chance in obtaining compelling evidence. An application of this concept is presented in the context of Bayesian Two-sample t-tests.

Keywords:

• Bayes factor
• Kullback-Leibler divergence
• hypothesis testing
• Bayesian two-sample t-test

Acknowledgments

This paper has benefited immensely from the lively discussions with Dr. Arthur Berg.