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

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 modeling uncertainties, which is particularly useful when the stationarity of a series can neither be ensured nor be totally rejected.