Bayes Factors as Uniformly Most Powerful Tests

Under quite mild assumptions, the Bayes factor for one-sided testing of the parameter of a statistical model is a monotone function of uniformly most powerful test statistics. Often closed-form formulas that connect Bayesian evidential thresholds of Bayes factors with the corresponding frequentist thresholds of optimal tests of given size are available. In these cases one can easily determine: (a) the operating characteristics (type-one error probability and power) of the Bayes factor for a given level of the evidence; (b) the evidential threshold induced by a chosen size for the test. The proposed method can also be used for prior criticism. We exemplify the above findings using the negative exponential model and data from a customer satisfaction study.