Dirichlet Mixtures for Multivariate Extremes: Re-Parametrization and Bayesian Inference with Censored Data

• Activity Number: 583
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anne Sabourin*+ and Philippe Naveau and Benjamin Renard
• Companies: Telecom ParisTech and Laboratoire des Sciences du Climat et de l'Environnement and Irstea
• Keywords: Multivariate extremes ; censored data ; semi parametric Bayesian inference ; mixture models ; Dirichlet mixture ; reversible-jump algorithm

Abstract

How to include censored data in a statistical analysis is a recurrent issue in statistics. In a multivariate extremes context, the dependence structure of large observations is non-parametric by nature, although it is common practice to restrict oneself to a parametric subclass. In this work, a exible semi-parametric Dirichlet mixture model for multivariate extremes is adapted to the context of censored data and missing components. One major issue is to take into account censoring intervals overlapping the extremal threshold, because it is unclear whether the corresponding hidden data sould be considered extreme or not. Further, The censored likelihood, which is needed for Bayesian inference, has no analytic expression. The rst issue is tackled using a Poisson process model and 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.