  The aim of this article is to make a contribution to the Bayesian procedure
of testing precise hypotheses for parametric models. For this purpose, we
define the Bayesian Discrepancy Measure that allows one to evaluate the
suitability of a given hypothesis with respect to the available information
(prior law and data). To summarise this information, the posterior median is
employed, allowing a simple assessment of the discrepancy with a fixed
hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a
single hypothesis with the observed data, as opposed to the more common
comparative approach where a hypothesis is rejected in favour of a competing
hypothesis. The proposed measure of evidence has properties of consistency and
invariance. After presenting the definition of the measure for a parameter of
interest, both in the absence and in the presence of nuisance parameters, we
illustrate some examples showing its conceptual and interpretative simplicity.
Finally, we compare the BDT with the Full Bayesian Significance Test, a
well-known Bayesian testing procedure for sharp hypotheses.
