Statistical Modeling of Spatial Extremes
Mathieu Ribatet, Anthony C. Davison, Simone A. Padoan
Department of Mathematics, University of Montpellier II, France; Institute of Mathematics, EPFL, Lausanne, Switzerland; EFLUM, EPFL, Lausanne, Switzerland

The areal modelling of the extremes of a natural process such as rainfall or tempera- ture is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statis- tical modelling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a dataset on rainfall in Switzerland. Whereas latent variable modelling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modelling of extremes.

Keywords: Environmental data analysis; Statistics of extremes; Bayesian hierarchical model; Max-stable pro- cess

Biography: I'm interested in extreme value theory and did most of my recent works in trying to proposal statistical models for spatial extremes mainly for environmental applications.