  Predicting extreme events is important in many applications in risk analysis.
The extreme-value theory suggests 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 paper 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, which
represents the most realistic inferential setting.
