Evidence and credibility: Full Bayesian signifiance test for precise hypotheses (Q1612919)

Summary: A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the `highest posterior density region' that is `tangent' to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the `tangent' region.