Bayesian inferences for an accelerated degradation model based on tweedie exponential dispersion process

Tweedie exponential dispersion (TED) process is a large class of generalized stochastic process, which includes the commonly used Wiener process, Gamma process and inverse Gausssian process as special cases. In this paper, we propose an accelerated degradation model based on the TED process, and then apply the objective Bayesian method to make inferences on the model. The Jeffreys prior and reference priors under different group orderings are derived, and the posterior property based on each prior is then validated. A simulation study is carried out to assess the performance of the proposed Bayesian method in comparison with the maximum-likelihood estimation (MLE), and finally the method is applied to analyse a real degradation dataset.