Exact simulation of max-stable processes

• 成果类型: Article
• 署名作者: Dombry, Clement; Engelke, Sebastian; Oesting, Marco
• 署名单位: Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Universitat Siegen
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw008
• 发表日期: 2016
• 页码: 303317
• 关键词: DISTRIBUTIONS; inference

摘要

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.