A likelihood-free approach towards Bayesian modeling of degradation growths using mixed-effects regression

Abstract

Mixed-effects regression models are widely applicable for predicting degradation growths in structural components. The Bayesian inference method is used to estimate the regression parameters when the degradation data are confounded by measurement and parameter uncertainties. The Gibbs sampler (GS), commonly used for this purpose, works when the regression errors are assumed as normally distributed that allows for the analytical formulation of the likelihood function. In case of a more general regression error distribution (e.g., mixture models), the likelihood becomes analytically intractable and computationally expensive to a degree that any likelihood-based Bayesian inference scheme (e.g., GS, Metropolis-Hastings sampler) can no longer be used for solving a practical problem.This paper proposes a practical likelihood-free approach for parameter estimation based on the approximate Bayesian computation (ABC) method. The ABC method implements forward simulation coupled with a rejection mechanism to sample from a target posterior distribution thereby eliminating the need to evaluate the likelihood function. The advantages of the proposed method are illustrated by analyzing degradation data obtained from a Canadian nuclear power plant.