关键词: 水文时间序列, 水文频率分析, 贝叶斯因子, 最大熵原理

Abstract:

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.

Key words: hydrologic time series, hydrologic frequency analysis, Bayesian factor, principle of maximum entropy