Simulation, Bayes, and bootstrap in statistical hydrology

Statistical simulation in hydrology is discussed from a Bayesian perspective. The inherent difficulties in both parametric simulation, based on a parent distribution, and classical nonparametric simulation, based on the bootstrap, are discussed. As an alternative to these procedures, a nonparametric Bayesian simulation methodology, Polya resampling, is introduced. Tt consists of simulating from a nonparametric predictive distribution obtained from the analysis of a reference sample, and it is asymptotically equivalent to the bootstrap. The method is generalized to take into account a prior hypothesis on the parametric distribution of a variable. A hybrid simulation model is then obtained that 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 models for flood frequency analysis. Tn this paper an example is used to demonstrate how Polya resampling can help assess the influence of a distribution hypothesis on simulation results.