Spatial Extremes: Inference and Some Thoughts Beyond Max-Stability

• Activity Number: 400
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Jenny Wadsworth*+ and Jonathan Tawn
• Companies: Ecole Polytechnique Federale de Lausanne and Lancaster University
• Keywords: Max-stable process ; inference ; spatial extremes

Abstract

Max-stable processes form one useful characterization of for extreme values of spatial processes. Inference for these processes has been largely restricted to pairwise composite likelihoods, due partially to intractability of higher dimensional distributions, and partially to the very large number of summands involved in higher dimensional densities. We discuss the application of a censored Poisson process likelihood, which cuts the number of summands down to one. For a large class of max-stable processes based on log-Gaussian random functions, we are able to calculate neat forms for all the required terms, and thus make inference practicable in $d$-dimensions. Max-stable processes are not however applicable as models for extreme values of all spatial processes. Those exhibiting the phenomenon of asymptotic independence require alternative strategies, which we also discuss.