Application of Bayesian approach to hydrological frequency analysis

An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three （P-III） probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo （MCMC） sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm （i.e. the important sampling） used in the existing approach, we use the adaptive metropolis （AM） sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.