当前位置: X-MOL 学术Probab. Eng. Inf. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
BAYESIAN ANALYSIS OF DOUBLY STOCHASTIC MARKOV PROCESSES IN RELIABILITY
Probability in the Engineering and Informational Sciences ( IF 1.1 ) Pub Date : 2020-04-08 , DOI: 10.1017/s0269964820000157
Atilla Ay , Refik Soyer , Joshua Landon , Süleyman Özekici

Markov processes play an important role in reliability analysis and particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the generator is also stochastic. In our model, we suppose that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. In fact, we have a Markov modulated Markov process which can be modeled as a bivariate Markov process that can be analyzed probabilistically using Markovian analysis. In this setting, however, we are interested in Bayesian inference on model parameters. We present a computationally tractable approach using Gibbs sampling and demonstrate it by numerical illustrations. We also discuss cases that involve complete and partial data sets on both processes.

中文翻译:

可靠性中双随机马尔可夫过程的贝叶斯分析

马尔可夫过程在可靠性分析中发挥重要作用,特别是在系统生存/故障行为的随机演化建模中。马尔可夫过程的概率定律由它的生成器或转移率矩阵来描述。在本文中,我们假设该过程是双重随机的,因为生成器也是随机的。在我们的模型中,我们假设生成器中的条目随着另一个马尔可夫过程的状态变化而变化。这个过程代表了随机模型运行的随机环境。事实上,我们有一个马尔科夫调制马尔科夫过程,它可以建模为一个二元马尔科夫过程,可以使用马尔科夫分析进行概率分析。然而,在这种情况下,我们对模型参数的贝叶斯推理感兴趣。我们提出了一种使用 Gibbs 采样的计算上易于处理的方法,并通过数值插图进行演示。我们还讨论了涉及两个过程的完整和部分数据集的案例。
更新日期:2020-04-08
down
wechat
bug