Bayesian Hypothesis Testing: Redux

TL;DR

This paper revisits Bayesian hypothesis testing by focusing on the distribution of the test statistic under the alternative hypothesis, offering a practical and interpretable default Bayes factor with real-world examples.

Contribution

It introduces a new approach to Bayesian hypothesis testing based on the observable test statistic distribution, simplifying interpretation and application.

Findings

Evidence can support the null hypothesis even when classical tests reject it.

The proposed method provides a straightforward default Bayes factor.

Illustrative examples demonstrate the method's practical utility.

Abstract

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter values, we provide a practical default Bayes factor which is straightforward to interpret. To illustrate our methodology, we provide examples where evidence for a Bayesian strikingly supports the null, but leads to rejection under a classical test. Finally, we conclude with directions for future research.