Abstract:
Connections between uniformly most powerful Bayesian tests and classical uniformly most powerful tests are used to equate the rejection regions of these two types of tests in order obtain an approximate equivalence between Bayes factors and p-values.  The implications of this equivalence for the reproducibility of scientific research are examined.  Approximately uniformly most powerful Bayesian tests are described for t tests, and the power of these tests are compared to ideal Bayes factors (defined by determining the best test alternative for each true value of the parameter), as well as to Bayes factors obtained using the true parameter value as the alternative.  Finally, extensions of uniformly most powerful tests outside of the class of exponential family models are discussed, and the concept of restricted most powerful Bayesian test is introduced and discussed.

* Joint work with Scott Goddard

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