基于MCMC稳态模拟的指数回归模型及其应用

讨论了加速失效模型族中最简单而又十分重要的指数回归模型，利用贝叶斯方法提高了该模型的有效性。为了较好的解决高维数值积分在实际应用中的难题，提出了对寿命服从指数分布的产品，运用基于Gibbs抽样的马尔科夫链蒙特卡洛（Markov Chain Monte Carlo，MCMC）方法动态模拟出参数后验分布的马尔科夫链，在回归参数的先验分布为多元正态分布时，给出随机截尾条件下，回归参数在指数回归模型中的贝叶斯估计，提高了计算的精度。借助数据仿真分析说明了利用WinBUGS（Bayesian inference Using Gibbs Sampling）软件包进行建模分析的过程，证明了该模型在可靠性应用中的直观性与有效性。

Exponential Regression Model Based on MCMC Method and Its Application

This paper discusses the exponential regression model, which is the simplest but very important in the family of Bayesian accelerated failure-time model. In order to resolve the difficulties of the high-dimension numerical integral better, as for the productions whose life distribution belongs to exponential distribution, this paper brings forward the MCMC method based on Gibbs sampling to simulate dynamically the Markov Chain of the parameters' posterior distribution. It gives the parameters' Bayesian estimation of the exponential regression model in the condition of the random truncated test when the prior distribution of the failure rate belongs to the Normal distribution, and improves the precision of the numeration. Also it utilizes the data's simulation to show the process of setting the model by using the WinBUGS package, and proves the objectivity and validity of the model.