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Name: Stefano Rizzelli

Talk Title: Consistency of Bayesian and empirical Bayesian inference on multivariate max-stable distributions

Abstract: Predicting extreme events is important in many applications in risk analysis. Under mild assumptions, extreme-value theory justifies modelling extremes by max-stable distributions. 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. In this contribution we focus on a semiparatric Bayesian method for estimating max-stable distributions in arbitrary dimension. We establish consistency of the pertaining posterior distributions for fairly general, well-specified max-stable models, 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, resorting to data-dependent prior distributions.

This talk is a contributed talk at EVA 2021. View the programme here.