On the correspondence between frequentist and Bayesian tests

Modern theory for statistical hypothesis testing can broadly be classified as Bayesian or frequentist. Unfortunately, one can reach divergent conclusions if Bayesian and frequentist approaches are applied in parallel to analyze the same data set. This is a serious impasse since there is a lack of consensus on when to use one approach in detriment of the other. However, this conflict can be resolved. The present paper shows the existence of a perfect equivalence between Bayesian and frequentist methods for testing. Hence, Bayesian and frequentist decision rules can always be calibrated, in both directions, in order to present concordant results.