Speaker
Description
In extreme value theory, the dependence structure between multivariate exceedances over a high threshold is fully characterised by their projections on the unit simplex. Under mild conditions, the only constraint on these angular variables is that their marginal means are equal. Their distribution functions thus form a non-parametric class within which deriving flexible and easy to use models is challenging, especially in high dimensions. Dirichlet mixtures are natural candidates to approximate such functions, but they are not necessarily valid angular distributions themselves. Previous approaches constrained the Dirichlet parameters in order to enforce the marginal mean property but the implementation of such models tends to be too slow especially in high dimensions. Instead of constraining the parameters, we let them vary freely and apply a transformation to the whole mixture in order to tilt the marginal means towards their desired values. The tilted mixtures of Dirichlet distributions are a new class of functions that are dense in the space of angular distributions and well-defined in all dimensions. We propose an MCMC procedure which is fast in all dimensions and does not require fine tuning. Furthermore, the mixture captures heterogeneity in the extremal dependence structure and allow the probabilistic clustering of observations. We demonstrate the performance of the proposed model on simulated data and show its usefulness on financial applications.
