%0 Journal Article %1 springerlink:10.1007/s00477-006-0047-4 %A Renard, Benjamin %A Lang, Michel %A Bois, Philippe %C Berlin / Heidelberg %D 2006 %I Springer %J Stochastic Environmental Research and Risk Assessment %K Bayesian Extremes MCMC Nonstationarity POT %P 97-112 %R 10.1007/s00477-006-0047-4 %T Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data %U http://dx.doi.org/10.1007/s00477-006-0047-4 %V 21 %X 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.

@article{springerlink:10.1007/s00477-006-0047-4, 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.}, added-at = {2011-01-31T12:22:53.000+0100}, address = {Berlin / Heidelberg}, affiliation = {Cemagref Centre de Lyon U.R. Hydrologie-Hydraulique 3 bis Quai Chauveau CP 220 69336 Lyon cedex 09 France}, author = {Renard, Benjamin and Lang, Michel and Bois, Philippe}, biburl = {https://www.bibsonomy.org/bibtex/2f46b199cad173ab64e4821db4ce3f86c/marsianus}, description = {SpringerLink - Stochastic Environmental Research and Risk Assessment, Volume 21, Number 2}, doi = {10.1007/s00477-006-0047-4}, interhash = {3caca3264cc63649bd6e1c454c5c9a37}, intrahash = {f46b199cad173ab64e4821db4ce3f86c}, issn = {1436-3240}, issue = {2}, journal = {Stochastic Environmental Research and Risk Assessment}, keyword = {Engineering}, keywords = {Bayesian Extremes MCMC Nonstationarity POT}, pages = {97-112}, publisher = {Springer}, timestamp = {2013-11-18T15:47:52.000+0100}, title = {Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data}, url = {http://dx.doi.org/10.1007/s00477-006-0047-4}, volume = 21, year = 2006 }