Neyman–Pearson lemma for Bayes factors

We point out that the Neyman–Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximizes the expected power for a fixed expected type-1 error rate. For Bayes factors involving a simple null hypothesis, the expected type-1 error rate is just the completely frequentist type-1 error rate. Lastly we remark on connections between the Karlin–Rubin theorem and uniformly most powerful tests, and Bayes factors. This provides frequentist motivations for computing the Bayes factor and could help reconcile Bayesians and frequentists.