  Uniformly most powerful tests are statistical hypothesis tests that provide
the greatest power against a fixed null hypothesis among all tests of a given
size. In this article, the notion of uniformly most powerful tests is extended
to the Bayesian setting by defining uniformly most powerful Bayesian tests to
be tests that maximize the probability that the Bayes factor, in favor of the
alternative hypothesis, exceeds a specified threshold. Like their classical
counterpart, uniformly most powerful Bayesian tests are most easily defined in
one-parameter exponential family models, although extensions outside of this
class are possible. 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. Finally, issues regarding the
strong dependence of resulting Bayes factors and p-values on sample size are
discussed.
