Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Stochastic Environmental Research and Risk Assessment Year : 2006

Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data

Benjamin Renard
M. Lang

Abstract

Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution.
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Dates and versions

hal-00452224 , version 1 (01-02-2010)

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Benjamin Renard, M. Lang, P. Bois. Statistical analysis of extreme events in a nonstationary context via a Bayesian framework. Case study with peak-over-threshold data. Stochastic Environmental Research and Risk Assessment, 2006, 21 (2), p. 97 - p. 112. ⟨10.1007/s00477-006-0047-4⟩. ⟨hal-00452224⟩
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