Bayesian Nonparametric Point Process Modeling for Extreme Value Analysis

• Activity Number: 319
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Athanasios Kottas*+ and Ziwei Wang and Abel Rodriguez and Bruno Sanso
• Companies: University of California, Santa Cruz and University of California, Santa Cruz and University of California, Santa Cruz and University of California, Santa Cruz
• Keywords: Dirichlet process mixtures ; Markov chain Monte Carlo ; Non-homogeneous Poisson process ; Spatial nonparametric priors

Abstract

We present a Bayesian nonparametric modeling framework for extreme values based on the point process approach for extremes. Under this approach, the bivariate point pattern comprising the exceedance times and the corresponding excess values arises (approximately) from a non-homogeneous Poisson process (NHPP). We develop a nonparametric mixture model that characterizes the intensity of extreme values. The model is built from Dirichlet process mixing for the NHPP density. Particular emphasis is placed on the choice of the Dirichlet process mixture kernel to achieve model flexibility and to provide connections with theoretical results regarding the tail behavior of the variable whose extremes are studied. We also discuss spatial modeling of extremes through nonparametric models for spatially related NHPP intensities. The methodology is illustrated with environmental data sets.