Bayes修正幂验前方法在制导精度评定中的应用

A Bayesian Modified Power Prior Approach with Applications in Guidance Precision Evaluation

如何合理有效的利用验前信息,是小子样评定中的关键问题。针对导弹制导精度评定,引入修正幂验前分布控制验前信息对验后估计的影响,详细推导了Bayes修正幂验前下的制导精度评定中兴趣参数的验后密度函数。通过对参数验后估计的分析,该方法能够有效避免验前信息'淹没'现场信息的情况,而幂参数通过验后边缘分布得到。通过对验后估计平均平方误差(MSE)的分析,给出了验前信息利用的一些基本原则,为工程应用提供了指导。

How to use prior information effectively and reasonably in Bayesian method, which is a critical problem in small sample evaluation. For evaluation if the guidance precise of missile, the paper introduces power prior parameter to control the effect of the prior information acting on the post estimation, and deduces detailedly post density function of interesting parameters by Bayesian method based on the modified power prior distribution. The new method can avoid effectively the scene that the prior data inundate the post data through analyzing the posterior estimation of interesting parameters, at the same time, the power parameter can be obtained from posterior marginal distribution. Some elementary principles about using the prior data are brought forward through calculating the mean square error of post estimation.