论文部分内容阅读
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。
In order to overcome the two difficult problems of linear selection and integration of hydrological frequencies, the priori distribution of parameters in solving Bayesian factors and the numerical integral of linear edge distribution, Bayesian sampling method and maximum entropy principle (POME ) To solve the parameter posterior distribution expression, and then apply the sample-by-sample approximate summation method to replace the linear edge distribution integral process in parameter sampling result, and then a new method for solving Bayesian factor is established. Case studies and Monte-Carlo statistical tests verify the accuracy and effectiveness of the proposed method. The results of the analysis show that the length of the sequence and the value of the parameters have a great influence on the results of the Bayesian and hydrological linear posterior probabilities. Because the essence of the BIC is to find a set of optimal parameters for Bayesian Therefore, when the unfavorable factors are affected, the estimation results of the parameters often have large errors, which leads to the large deviation of the analysis results of the BIC criterion. The new method of solving Bayesian factor can overcome the influence of the above unfavorable factors, the parameter uncertainty can be analyzed and described reasonably, and the result of analysis and calculation can be obviously improved. Therefore, the new method has better practicability and reliability.