Efficient inference for spatial extreme value processes associated to log-Gaussian random functions

Wadsworth, Jennifer and Tawn, Jonathan (2014) Efficient inference for spatial extreme value processes associated to log-Gaussian random functions. Biometrika, 101 (1). pp. 1-15. ISSN 0006-3444

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Abstract

Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class of models for the extreme values of spatial processes. Until recently, inference for max-stable processes has been restricted to the use of pairwise composite likelihoods, due to intractability of higher-dimensional distributions. In this work we consider random fields that are in the domain of attraction of a widely used class of max-stable processes, namely those constructed via manipulation of log-Gaussian random functions. For this class, we exploit limiting d-dimensional multivariate Poisson process intensities of the underlying process for inference on all d-vectors exceeding a high marginal threshold in at least one component, employing a censoring scheme to incorporate information below the marginal threshold. We also consider the d-dimensional distributions for the equivalent max-stable process, and perform full likelihood inference by exploiting the methods of Stephenson & Tawn (2005), where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood. The Stephenson–Tawn likelihood is in fact simply a special case of the censored Poisson process likelihood. We assess the improvements in inference from both methods over pairwise likelihood methodology by simulation.

Item Type:
Journal Article
Journal or Publication Title:
Biometrika
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1100/1100
Subjects:
?? extreme value theorylikelihood inferencemax-stable processpoisson processspatial extremegeneral agricultural and biological sciencesapplied mathematicsstatistics and probabilitystatistics, probability and uncertaintygeneral mathematicsagricultural and bio ??
ID Code:
73874
Deposited By:
Deposited On:
18 Jun 2015 05:55
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 09:44