Statistical Modeling of Spatial Extremes

TL;DR

This paper reviews recent statistical methods for modeling spatial extremes like rainfall and temperature, emphasizing the importance of max-stable processes and copulas for accurate joint distribution modeling.

Contribution

It compares latent variable, copula, and max-stable models for spatial extremes, highlighting their strengths and limitations in environmental data analysis.

Findings

Latent variable models fit marginal distributions well.

Copula and max-stable models better capture joint extremes.

Application to Swiss rainfall data demonstrates model differences.

Abstract

The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statistical modeling 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 data set on rainfall in Switzerland. Whereas latent variable modeling 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 modeling of extremes.