Bayesian clustering of multivariate extremes

The asymptotic dependence structure between multivariate extreme values is fully characterized by their projections on the unit simplex. Under mild conditions, the only constraint on the resulting distributions is that their marginal means must be equal, which results in a nonparametric model that can be difficult to use in applications. Mixtures of Dirichlet distributions have been proposed for use as a semiparametric model, but fitting them is awkward. In this article, we propose a new approach to the use of Dirichlet mixtures, based on tilting, to ensure that the moment conditions are satisfied. We show that these tilted mixtures are dense in the full nonparametric family, are well defined in all dimensions, and allow the probabilistic clustering of extreme events. In order to fit them, we use a fast Markov chain Monte Carlo algorithm that does not require fine‐tuning. Its performance is assessed using simulations and an application to financial data.