Fast Bayesian Inference of Reparameterized Gamma Process With Random Effects

In the field of reliability engineering, the gamma process plays an important role in modeling degradation processes. However, extracting lifetime information from product degradation observations has long been suffering from both ineffective modeling techniques and inefficient statistical inference methods. To overcome these challenges, we propose a reparameterized gamma process with random effects in this article. Compared with the classical gamma process, the proposed model has a more intuitive physical interpretation. In addition, statistical inference for the model can be readily done through the variational Bayesian algorithm. Combining with the Gauss–Hermite quadrature and the Laplace approximation, the algorithm yields closed-form variational posteriors for the proposed model. Its superiority over two other inference methods (expectation maximization and Monte Carlo Markov Chain) in terms of computational efficiency and estimation accuracy is demonstrated by simulation.