基于共轭分布的飞行器试验贝叶斯统计方法

Bayes Statistics Method for Aircraft Testing Data Based on Conjugate Distribution

针对飞行器试验数据总体分布参数均未知,无法直接使用Bayes方法得到验后分布的情况,提出先采用随机加权得到历史数据验前分布,然后用Bayes方法估计出总体方差,最后运用共轭先验分布得到均值验后分布的方法。仿真结果表明:分布参数置信区间减小,估计精确度增加,避免了直接使用Bayes估计算法复杂、无法积分的问题,是解决验前信息不足、分布参数未知情况下进行飞行器试验数据Bayes估计的一种有效途径。

Because of the general distribution parameter of aircraft testing data is unknown,Bayes theory can not obtain posterior distribution.We put forward conjugate distribution theory to solve this problem.First,prior distribution of historical data was obtained by stochastic weighting,and then population variance was calculated by Bayes theory.Posterior distribution of mean was estimated by conjugate distribution theory.The simulation showed that confidence interval of distribution parameter decreased and precision of estimating increased.This approach avoided the problem of arithmetic complexity caused by Bayes theory directly,and unable to integral.It was an efficient way to process aircraft test data under the condition of prior information insufficiency and distribution parameter unknown.