基于新Dirichlet先验分布的超参数确定方法研究

研究了基于新Dirichlet先验分布的Bayesian可靠性增长模型的超参数 确定方法，该方法将专家经验表示为均匀分布，以先验参数为变量，将均值作为约束条件、 方差作为目标，利用最优化方法求出与该均匀分布最为接近的Beta分布，解决了由于新
Dirichlet先验分布超参数物理意义不明确而难以确定的问题。针对后验积分难以计算的问 题，采用WinBUGS软件建立了新Dirichlet先验分布的Bayesian可靠性增长模型，该模型思路 清晰、简单易行，提高了计算的精度，实例证明了该模型在可靠性应用中的直观性与有效性 。

A Method to Determine the Hyper Parameters of the New Dirichlet Prior Distribution

This article studies on determining method for the hyper parameters of the new Dirichlet prior distribution.Based on the new Dirichlet prior distribution,expert experience is simply described as uniform distribution,the prior parameters is treated as variables,and the mean is used as constraint condition,furthermore the variance is treated as the optimization objective equivalent Beta distribution of uniform distribution is found out by the method of optimization,it solves the problem of how to verify the hyper parameters of the new Dirichlet prior distribution because of these parameters having no specific physical meaning.Because the posterior integral is very difficult to calculate,WinBUGS software package is used to construct the Bayesian reliability growth model of the new Dirichlet prior distribution,and the numerical simulation is used for this model.The analysis result of practical cases proves the objectivity and validity of the model,and shows that the model can improve the precision of the calculation,and it is easy to be used in engineering.