The flaw of averages: Bayes factors as posterior means of the likelihood ratio

Abstract

As an alternative to the Frequentist p-value, the Bayes factor (or ratio of marginal likelihoods) has been regarded as one of the primary tools for Bayesian hypothesis testing. In recent years, several researchers have begun to re-analyze results from prominent medical journals, as well as from trials for FDA-approved drugs, to show that Bayes factors often give divergent conclusions from those of p-values. In this paper, we investigate the claim that Bayes factors are straightforward to interpret as directly quantifying the relative strength of evidence. In particular, we show that for nested hypotheses with consistent priors, the Bayes factor for the null over the alternative hypothesis is..