Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all possible tests of a given size. In this article, I extend the notion of uniformly most powerful tests by defining a uniformly most powerful Bayesian test to be a test which maximizes the probability that the Bayes factor in favor of the alternative hypothesis exceeds a given threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although I demonstrate that extensions outside of this class are possible. I also show how the connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between p-values and Bayes factors. Several examples of these new Bayesian tests are provided.
Johnson, Valen E., "Uniformly Most Powerful Bayesian Tests" (July 2012). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 74.