水文频率线型选择与综合过程中贝叶斯因子求解新方法

为克服水文频率线型选择和综合过程中,贝叶斯因子求解时参数先验分布确定和线型边缘分布数值积分这两个难点问题,联合应用了贝叶斯采样方法和最大熵原理(POME)求解参数后验分布表达式,然后应用参数采样结果中逐个样本近似求和方法代替线型边缘分布积分过程,进而建立了贝叶斯因子求解新方法。实例分析和Monte-Carlo统计试验验证了该方法的准确性和有效性。分析结果显示:序列长度和参数取值大小等因素对贝叶斯因子和水文线型后验概率求解结果影响较大;由于BIC准则的实质是通过寻求一组最优参数值进行贝叶斯因子求解,因此在受到不利因素影响时参数估计结果往往存在较大误差,使得BIC准则的分析结果也存在较大偏差。贝叶斯因子求解新方法能够克服上述不利因素的影响,可以合理地分析和描述参数不确定性,使得分析计算结果明显改善,因此所提新方法具有更好的实用性和可靠性。

New Method of Bayesian Factor Computation in Hydrologic Frequency Model Selections and Averages

For solving the two difficult problems about Bayesian factor computation (i.e., determination of parameters prior distribution and numerical integration of hydrologic frequency model) in the process of hydrologic frequency model selections and averages, this paper firstly combined the Bayesian sampling method with POME (principle of maximum entropy) to determine the expression of parameters posterior distribution, and then the method of approximate sums after interval segmentation was used instead of the numerical integration of hydrologic frequency model, finally a new method of Bayesian factor computation was proposed. The accuracy and effectiveness of the new method have been verified by both observed hydrologic series analyses and Monte-Carlo tests. The results show that series length and parameters values have great influences on the computation results of Bayesian factor and models posterior probability. The essence of Bayesian information criterion (BIC) is to compute the Bayesian factor by using a group of best parameters estimation results; whenever unfavorable factors are encountered, the analyses results of BIC would become bad due to the inaccurate parameters estimation results. Compared with the BIC criterion, the new method is more effective and reliable, since it can overcome the influence of those unfavorable factors by analyzing and describing the uncertainties of model parameters.