A natural conjugate prior for the nonhomogeneous poisson process with an exponential intensity function
A natural conjugate prior for the nonhomogeneous poisson process with an exponential intensity function
复制标题
具有指数强度函数的非齐次泊松过程的自然共轭先验
DOI：
10.1080/03610929908832368
复制
发表时间：
1999
影响因子：
0.8
通讯作者：
V. Bier
中科院分区：
文献类型：
--
作者：
Yeu;V. Bier
针对具有指数强度函数的非齐次泊松过程(NHPP)，提出了一种自然共轭先验，用于建模可修系统的故障率。研究了共轭先验分布关于其参数的行为，并将其在贝叶斯估计中的应用与其他两种估计方法(使用独立的先验分布和二元正态分布)进行了比较。这里提出的共轭先验的使用方便了老化的贝叶斯统计分析。特别是，建议的先验允许我们明确地考虑初始故障率和老化速率之间的相关性。这是对大多数以前工作中所做的假设的显著改进(要么假设老化速率已知，要么假设初始故障率和老化速率是独立的)。蒙特卡罗模拟表明，使用所提出的先验的贝叶斯估计的性能通常至少与我们所提出的先验估计相同。
This article presents a natural conjugate prior for the nonhomogeneous Poisson process (NHPP) with an exponential intensity function, for modeling the failure rate of repairable systems. The behavior of the conjugate prior distribution with respect to its parameters is studied, and the use of this prior in Bayesian estimation is compared to two other estimation approaches (the use of independent prior distributions, and the bivariate normal distribution). The use of the conjugate prior proposed here facilitates Bayesian statistical analysis of aging. In particular, the proposed prior allows us to explicitly account for dependence between the initial failure rate and the aging rate. This is a significant improvement over the assumptions made in most prior work (either the assumption that the aging rate is known, or the assumption that the initial failure rate and the aging rate are independent). Monte Carlo simulation shows that Bayesian estimation using the proposed prior generally performs at least as we...