Application of Bayesian approach to hydrological frequency analysis

Department of Geosciences, University of Nevada, Las Vegas, NV 89154, USA
Science China Technological Sciences (Impact Factor: 1.19). 05/2011; 54(5):1183-1192. DOI: 10.1007/s11431-010-4229-4


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

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Available from: Binquan Li, Dec 22, 2014
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    • "Lee and Kim [13] employed the Bayesian Markov Chain Monte Carlo (MCMC) method and the maximum likelihood estimation (MLE) to assess uncertainties of low-flow frequency analysis. Zhongmin et al. [14] [15] applied the Bayesian theory to separately analyze the impact of parameters uncertainty and both frequency model and parameters uncertainties on the uncertainties of estimation of design value or quantile. However, studies on the impact of the sample representativeness on the uncertainty of design value estimation have been seldom reported. "
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