Unified Bayesian and Conditional Frequentist Testing for Discrete Distributions

Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of datadependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the actual amount of evidence in the observed data. The resulting randomized tests are also seen to be Bayesian tests, in the strong sense that the reported error probabilities are also the posterior probabilities of the hypotheses. The new procedure is illustrated for a variety of testing situations, both simple and composite, involving discrete distributions. Testing linkage heterogeneity with the new procedure is given as an illustrative example.