探讨了贝叶斯理论在水文频率分析计算中的应用。根据贝叶斯公式耦合先验和样本信息,采用Markov chain Monte Carlo(MCMC)抽样技术估计参数的后验分布,并通过参数的随机样本构造设计值的抽样分布,根据设计值的抽样分布可以推求设计值的点估计和区间估计。与传统水文频率分析方法相比,基于贝叶斯理论的分析方法不仅能提供设计值的各种估计,同时能够对估计的不确定性进行定量评价,为水文频率分析计算提供更丰富的信息。
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.
