Semi-parametric Modelling of Excesses above High Multivariate Thresholds with Censored Data

One commonly encountered problem in statistical analysis of extreme events is that very few data are available for inference. This issue is all the more important in multivariate problems that the dependence structure among extremes has to be inferred. In some cases, e.g. in environmental applications, it is sometimes possible to increase the sample size by taking into account historical or incomplete series with partial censoring. In this work, a semi-parametric Dirichlet mixture model for multivariate extremes is adapted to the context of censored data and missing components. The censored likelihood, which is needed for Bayesian inference, has no analytic expression. A data augmentation scheme is introduced, which avoids multivariate integration of the Poisson process intensity over both the censored intervals and the failure region above threshold. Multivariate extremes; censored data; semi parametric Bayesian inference; mixture models; Dirichlet mixture; reversible-jump algorithm.