SIMULATION, BAYES, AND BOOTSTRAP IN STATISTICAL HYDROLOGY

Statistical simulation in hydrology is discussed from a Bayesian persp ective. The inherent difficulties in both parametric simulation, based on a parent distribution, and classical nonparametric simulation, bas ed on the bootstrap, are discussed. As an alternative to these procedu res, a nonparametric Bayesian simulation methodology, Polya resampling , is introduced. Tt consists of simulating from a nonparametric predic tive distribution obtained from the analysis of a reference sample, an d it is asymptotically equivalent to the bootstrap. The method is gene ralized to take into account a prior hypothesis on the parametric dist ribution of a variable. A hybrid simulation model is then obtained tha t includes parametric and nonparametric simulation as particular cases . An extensive application is presented in a related paper [Fortin er al., 1997], where Polya resampling is used to compare statistical mode ls for flood frequency analysis. Tn this paper an example is used to d emonstrate how Polya resampling can help assess the influence of a dis tribution hypothesis on simulation results.