Full bayesian analysis for a model of tail dependence

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)The family of the asymmetric logistic copulas appears naturally in modeling tail dependence. Within this family, some well-known models, as independence and logistic dependence, define precise hypotheses, having zero posterior probability for an absolute continuous posterior distribution. We show that the e-value associated to the Full Bayesian Significance Test has a good performance in non standard dependence problems, obtaining posterior estimates and predictive distributions. The analysis proposed is illustrated with two examples: (1) monthly sea level maxima at Newlyn and Sheerness, England (1990-2005) and (2) AIDS rates related to an educational indicator in U. S. Census Bureau (2007). We validate the inferences obtained through simulated data.The family of the asymmetric logistic copulas appears naturally in modeling tail dependence. Within this family, some well-known models, as independence and logistic dependence, define precise hypotheses, having zero posterior probability for an absolute412241074123CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [485999/2007-2, 476501 2009-1]485999/2007-2; 476501 2009-

Full Bayesian significance test for extremal distributions

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.