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Conditional sampling for spectrally discrete max-stable random fields

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Yizao Wang  and
Stilian A. Stoev
Yizao Wang*
Affiliation:
University of Michigan
Stilian A. Stoev*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Statistics, University of Michigan, 439 West Hall, 1085 South University, Ann Arbor, MI 48109-1107, USA.
∗ Postal address: Department of Statistics, University of Michigan, 439 West Hall, 1085 South University, Ann Arbor, MI 48109-1107, USA.
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Abstract

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Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.

Keywords

Max-stable processspectrally discrete representationregular conditional probabilityMARMA processSmith modelset cover problem

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 65C50: Other computational problems in probability
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011 , pp. 461 - 483
Copyright
Copyright © Applied Probability Trust 2011 

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