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.

中文翻译：

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使用混合效应回归对退化增长进行贝叶斯建模的无似然方法

摘要 混合效应回归模型广泛适用于预测结构组件的退化增长。当退化数据被测量和参数不确定性混淆时，贝叶斯推理方法用于估计回归参数。Gibbs 采样器 (GS) 通常用于此目的，当回归误差被假定为正态分布时，允许似然函数的分析公式。在更一般的回归误差分布（例如，混合模型）的情况下，可能性在分析上变得难以处理且计算成本高到无法再使用任何基于可能性的贝叶斯推理方案（例如，GS、Metropolis-Hastings 采样器）的程度为了解决一个实际问题。本文提出了一种基于近似贝叶斯计算 (ABC) 方法的参数估计实用无似然方法。ABC 方法实现了前向模拟和拒绝机制，从目标后验分布中采样，从而消除了评估似然函数的需要。通过分析从加拿大核电厂获得的退化数据，说明了所提出方法的优点。