Full Bayesian significance test for extremal distributions

Abstract

A new Bayesian measure of evidence is used for model choice within the generalized extreme value family of distributions, given an absolutely continuous posterior distribution on the related parametric space. This criterion allows quantitative measurement of evidence of any sharp hypothesis, with no need of a prior distribution assignment to it. We apply this methodology to the testing of the precise hypothesis given by the Gumbel model using real data. Performance is compared with usual evidence measures, such as Bayes factor, Bayesian information criterion, deviance information criterion and descriptive level for deviance statistic.