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

Benjamin Renard (1) , M. Lang (1) , P. Bois (2)

1 UR HHLY - Hydrologie-Hydraulique
2 LTHE - Laboratoire d'étude des transferts en hydrologie et environnement

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.

Mots clés: ANALYSE STATISTIQUE; INCERTITUDE; CHANGEMENT CLIMATIQUE; THEORIE DES VALEURS EXTREMES; ANALYSE FREQUENTIELLE; STATIONNARITE; STATISTIQUE BAYESIENNE; METHODE MCMC; BAYESIAN ANALYSIS; EXTREME EVENTS; STATIONARITY; UNCERTAINTIES; CLIMATE CHANGE; FREQUENCY ANALYSIS

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Analyse de données, Statistiques et Probabilités [physics.data-an]; Probabilités [math.PR]; Climatologie; Milieux et Changements globaux

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⟩