改进先验概率的贝叶斯法在设计洪水中的应用

Application of Bayesian model with improved prior probability in design flood analysis

贝叶斯模型是降低设计洪水计算过程中线型选择不确定性的主要方法,其中,先验概率的确定对贝叶斯模型的建立至关重要。为了提高先验概率确定方法的普适性,本文以模型评价准则为基础,多方面考虑模型拟合特征,提出综合指数量化线型的拟合情况,并将其作为先验信息应用于贝叶斯模型,以便合理确定各线型的先验概率,进而达到降低线型选择不确定性影响的目的。研究结果表明:基于综合指数值来挖掘样本的先验信息,可获得较为可靠的先验概率值来合理预估后验概率,使得拟合效果较好的线型获得更高的权重;有先验信息的贝叶斯模型相比无先验信息的贝叶斯模型结果更优;耦合多个评价准则的综合指数值为先验概率的求解提供了新思路。

Bayesian model is a powerful tool for reducing model uncertainty in flood frequency analysis,and the key is how to calculate prior probability.To improve the universality of the calculation,first we work out a formula for calculating the comprehensive index and quantifying the effect of fitting used by different models based on model evaluation criteria.Then,this index is used in calculation of the prior probability adopted in our Bayesian model so as to reduce the uncertainty in model selection.Results show that the comprehensive index calculations lead to more reliable values of the prior probability that help improve the estimation of posterior probability,thereby reducing the uncertainty in flood frequency calculations.Compared with Bayesian model without such prior information,the present results are much better.A comprehensive index coupled with multiple evaluation criteria provides a new idea in determining prior probability.