Statistical Science

Statistical Modeling of Spatial Extremes

A. C. Davison, S. A. Padoan, and M. Ribatet

Full-text: Open access

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.

Article information

Source
Statist. Sci. Volume 27, Number 2 (2012), 161-186.

Dates
First available in Project Euclid: 19 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.ss/1340110864

Digital Object Identifier
doi:10.1214/11-STS376

Mathematical Reviews number (MathSciNet)
MR2963980

Keywords
Annual maximum analysis Bayesian hierarchical model Brown–Resnick process composite likelihood copula environmental data analysis Gaussian process generalized extreme-value distribution geostatistics latent variable max-stable process statistics of extremes

Citation

Davison, A. C.; Padoan, S. A.; Ribatet, M. Statistical Modeling of Spatial Extremes. Statist. Sci. 27 (2012), no. 2, 161--186. doi:10.1214/11-STS376. http://projecteuclid.org/euclid.ss/1340110864.


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See also

  • Discussion of: “Statistical Modeling of Spatial Extremes” by A. C. Davison, S. A. Padoan and M. Ribatet.
  • Discussion of: “Statistical Modeling of Spatial Extremes” by A. C. Davison, S. A. Padoan and M. Ribatet.
  • Discussion of: Nonparametric Inference for Max-Stable Dependence.
  • Discussion of: “Statistical Modeling of Spatial Extremes” by A. C. Davison, S. A. Padoan and M. Ribatet.
  • Rejoinder: Statistical Modeling of Spatial Extremes.