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An application of Bayesian analysis and Markov chain Monte Carlo methods to the estimation of a regional trend in annual maxima

Abstract : L'analyse bayésienne est de plus en plus utilisée en hydrologie, car elle offre un cadre méthodologique permettant d'intégrer des connaissances physiques et statistiques dans des modèles complexes. Cet article en présente une application dédiée à l'analyse régionale fréquentielle de valeurs extrêmes, dans un contexte non stationnaire. Les méthodes MCMC sont utilisées pour résoudre numériquement un problème multidimensionnel sur un ensemble de séries hydrométriques. L'article montre l'intérêt d'une analyse régionale vis à vis d'une estimation locale site par site. Le cadre bayésien d'analyse permet d'intégrer les incertitudes de modélisation, ce qui est particulièrement utile lorsque le diagnostic sur la stationnarité des séries ne peut être totalement accepté ou rejeté. / Bayesian analysis is becoming increasingly popular in a number of fields, including hydrology. It appears to be a convenient framework for deriving complex models in agreement with both physical reality and statistical requirements. The aim of this paper is to present an application to the regional frequency analysis of extremes in a nonstationary context. A nonstationary regional model is thus proposed, together with the related hypotheses. The Bayesian inference of this model is then described. Markov chain Monte Carlo (MCMC) methods are needed for this purpose because of the dimensionality of the model and are described in this paper. The usefulness of such a model is then illustrated on a hydrological case study concerning annual maximum discharges of several sites. The advantage of regional analysis compared to at-site estimation is thus highlighted. Moreover, the Bayesian framework allows for a direct and comprehensive inference based on the posterior distribution and is able to take into account modelling uncertainties, which is particularly useful when the stationarity of a series can neither be ensured nor be totally rejected.
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Benjamin Renard, V. Garreta, M. Lang. An application of Bayesian analysis and Markov chain Monte Carlo methods to the estimation of a regional trend in annual maxima. Water Resources Research, American Geophysical Union, 2006, 42, p. W12422 - p. ⟨10.1029/2005WR004591⟩. ⟨hal-00453882⟩

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