Application of Bayesian approach to hydrological frequency analysis
ABSTRACT 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.
KeywordsBayesian theory–hydrological frequency analysis–Markov Chain Monte Carlo–prior distribution–posterior distribution