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2017 Bayesian inference for multivariate extreme value distributions
Clément Dombry, Sebastian Engelke, Marco Oesting
Electron. J. Statist. 11(2): 4813-4844 (2017). DOI: 10.1214/17-EJS1367


Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families have been developed and successfully applied. Due to complicated likelihoods, the efficient statistical inference is still an active area of research, and usually composite likelihood methods based on bivariate densities only are used. Thibaud et al. (2016) use a Bayesian approach to fit a Brown–Resnick process to extreme temperatures. In this paper, we extend this idea to a methodology that is applicable to general max-stable distributions and that uses full likelihoods. We further provide simple conditions for the asymptotic normality of the median of the posterior distribution and verify them for the commonly used models in multivariate and spatial extreme value statistics. A simulation study shows that this point estimator is considerably more efficient than the composite likelihood estimator in a frequentist framework. From a Bayesian perspective, our approach opens the way for new techniques such as Bayesian model comparison in multivariate and spatial extremes.


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Clément Dombry. Sebastian Engelke. Marco Oesting. "Bayesian inference for multivariate extreme value distributions." Electron. J. Statist. 11 (2) 4813 - 4844, 2017.


Received: 1 August 2017; Published: 2017
First available in Project Euclid: 27 November 2017

zbMATH: 1383.62061
MathSciNet: MR3729660
Digital Object Identifier: 10.1214/17-EJS1367

Primary: 62F15
Secondary: 60G70 , 62F12

Keywords: asymptotic normality , Bayesian statistics , efficient inference , full likelihood , Markov chain Monte Carlo , max-stability , multivariate extremes


Vol.11 • No. 2 • 2017
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