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Abstract
The recent proliferation of Markov chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields. To facilitate MCMC applications, this paper proposes an integrated procedure for Bayesian inference using MCMC methods, from a reliability perspective. The goal is to build a framework for related academic research and engineering applications to implement modern computational-based Bayesian approaches, especially for reliability inferences. The procedure developed here is a continuous improvement process with four stages (Plan, Do, Study, and Action) and 11 steps, including: (1) data preparation; (2) prior inspection and integration; (3) prior selection; (4) model selection; (5) posterior sampling; (6) MCMC convergence diagnostic; (7) Monte Carlo error diagnostic; (8) model improvement; (9) model comparison; (10) inference making; (11) data updating and inference improvement. The paper illustrates the proposed procedure using a case study.
Highlights
The recent proliferation of Markov Chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields, including behavioural science, finance, human health, process control, ecological risk assessment, and risk assessment of engineered systems [1]
Note that this paper will focus on six steps and their relationship to MCMC inference implementation: (1) prior elicitation; (2) model construction; (3) posterior sampling; (4) MCMC convergence diagnostic; (5) Monte Carlo error diagnostic; (6) model comparison
Lin et al [10] present a new approach to reliability analysis for complex systems, in which a certain fraction of subsystems is defined as a “cure fraction” based on the consideration that such subsystems’ lifetimes are long enough or they never fail during the life cycle of the entire system; this is called the cure rate model
Summary
The recent proliferation of Markov Chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields, including behavioural science, finance, human health, process control, ecological risk assessment, and risk assessment of engineered systems [1]. Discussions of MCMC-related methodologies and their applications in Bayesian Statistics appear throughout the literature [2, 3]. Most of the literature emphasizes the model’s development; no studies offer a full framework to accommodate academic research and engineering applications seeking to implement modern computational-based Bayesian approaches, especially in the area of reliability. To fill the gap and to facilitate MCMC applications from a reliability perspective, this paper proposes an integrated procedure for the Bayesian inference.
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