Full Bayesian Analysis for a Model of Tail Dependence
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.