Objective Bayesian analysis for the accelerated degradation model based on the inverse Gaussian process

The inverse Gaussian process is an attractive stochastic process to model monotone degradation paths in degradation analysis. In this paper, we propose an objective Bayesian method to analyze the accelerated degradation model based on the inverse Gaussian process. Noninformative priors including the Jeffreys prior and reference priors are derived, and the propriety of the posteriors under each prior is validated. A simulation study is carried out to investigate the performance of the approach compared with the maximum likelihood method and the Bootstrap method. Numerical results show that the proposed method has better performance in terms of the mean squared error and the frequentist coverage probability. The reference prior ${\pi }_{R_2}$ is recommended to use in practice. Finally, the Bayesian approach is applied to a real data.