Linear versus logarithmic proposal updates in Bayesian Markov chain Monte Carlo sampling for failure rate estimation

Abstract

Rigorous reliability and Probabilistic Risk / Safety Assessment (PRA / PSA) of components in complex infrastructure systems is an important field of concern for civil engineering and related disciplines. Among the several modelling strategies available, there has been ongoing debate about the most robust techniques for estimating failure rates for components in nuclear power plants with such candidates as Bayes-Empirical-Bayes (BEB), Parametric-Robust-Empirical-Bayes (PREB) and Parametric-Empirical-Bayes (PEB). While existing methods offer some solutions, they also present notable deficiencies – particularly in their ability to manage uncertainty in failure rate estimation. One promising avenue for addressing this limitation is using Markov Chain Monte Carlo (MCMC) to estimate the hyperpriors of the Bayesian model. In this work we focus on the BEB model and investigate different MCMC sampling strategies for it, in particular comparing two possible scalings for the MCMC proposal kernel, linear versus logarithmic. While the primary motivation remains grounded in nuclear safety, the modelling framework and inference methods discussed in this study are broadly applicable and are sufficiently general to be transferred across civil, structural, and mechanical engineering domains.