Title: Consistency of Bayesian and empirical Bayesian inference on max-stable models
Authors: Stefano Rizzelli - Catholic University - Milan (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Abstract: Predicting the extremes of multiple variables is important in many applied fields. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. We establish the strong posterior consistency of a semiparametric Bayesian inferential procedure for well-specified max-stable models of arbitrary dimension, whose margins can be short-, light- or heavy-tailed. We then extend our consistency results to the case where the data come from a distribution lying in a neighbourhood of a max-stable one, representing a more realistic inferential setting. In doing this, we define a new hybrid-Bayesian approach, where data-dependent priors are specified in an empirical Bayes fashion. The developed technical tools appear of independent interest, beyond the context of the extreme values, and can be adapted to other statistical methods affected by a model convergence bias.