正态型位置参数Bayes估计中基于P值的验前分布可信度建模

Modeling for prior distribution's reliability based on P value in Bayes evaluation for location parameter of normal distribution

基于Bayes方法完成对战技指标的分析,首要和关键的问题是选择合理可信的验前分布.以正态分布位置参数的Bayes分析为研究对象,构建了基于P值的验前可信度计算模型.首先,对验前分布可信度研究的基本假设和必要性进行了阐述.然后,对于正态分布的位置参数,分为方差未知和已知两种情况,分别建立了基于t分布的验前P值计算模型,和基于正态分布的验前P值计算模型,并给出了不同验前可信度取值范围下验前分布的选择与判断准则.其次,对于正态分布的变形,构建了基于非中心t分布的验前P值计算模型,和基于正态分布的验前P值计算模型.通过四个示例对验前分布P值模型的构建和分析过程进行了阐述,验证了方法的有效性.

Selecting credible prior distribution is the primary and key problem in Bayes equipment tactical and technical index analysis. Took the Bayes analysis of normal distribution＇s location parameter as research object, the prior reliability model based on P value was constructed. Firstly, the basic assumption and necessity of prior distribution＇s reliability research was presented. Secondly, for the location parameter of normal distribution, the P value calculating models based on t distribution and normal distribution were presented respectively, when population variance was unknown or not. And the judgement and select method of prior distributions for different prior reliability values were given. Finally, for the deformation of normal distribution, the P value calculating models based on noncentral t distribution and normal distribution were carried out separately. With four examples, the process and validity of prior reliability calculating were illustrated.