基于贝叶斯理论的水文频率线型选择与综合

Selecting and averaging of flood frequency models based on Bayesian theory

针对水文频率分析中线型的不确定性问题,利用基于贝叶斯因子理论的模型选择与综合方法进行研究.介绍了利用贝叶斯因子进行模型选择、综合的理论与方法,通过统计试验,验证了贝叶斯模型选择在一定程度上能识别数据的真实线型.结合某水库坝址洪峰流量频率分析问题,采用5种常用线型作为备选线型进行线型选择与综合,结果表明:线型的后验概率越大则可拟合越好;贝叶斯模型综合能根据各线型的后验概率设置权重进行加权平均,以此减小线型选择的不确定性.

Focused on model uncertainty among frequency analysis by the method of Bayesian model selection and Bayesian model averaging （BMA）, the theory of Bayes factors approach to model selection and model averaging is introduced. Based upon the Monte Carlo experiments, the true model can be identified in most time, indicating that the performances of Bayesian model selection are efficient. A case study on the annual maximum discharges of a certain reservoir is discussed, which indicates that the BMA can fit the empirical plotting points very well by averaging probability distributions with posterior probability. The conclusions are drawn that the BMA is useful to deal with the model uncertainty in frequency analysis.