Bayesian Inference of Non-Stationary Flood Frequency Models

In this paper, the problem of fully Bayesian estimation of the extreme value model parameters is addressed. Extreme value models with covariates are an adapted tool to incorporate additional information given by dependence on the covariates or to represent trends in the time series. The Generalized Maximum Likelihood method (GML) is developed for the Generalized Extreme Value (GEV) and Generalized Pareto (GPD) models with covariates. In the GML method, the shape parameter of the GEV and GPD distributions has a Beta distribution as prior drawn for hydro-meteorological variables. This prior distribution is considered to make inference for both distributions in the case of a model with covariates in a fully Bayesian framework. The reversible jump MCMC (RJMCMC) procedure is developed in order to carry out both parameter estimation and Bayesian model selection. Real and simulated datasets are used to illustrate the proposed methodology.