Reference Bayesian analysis of inverse Gaussian degradation process

In this paper, objective Bayesian method is applied to analyze degradation model based on the inverse Gaussian process. Noninformative priors (Jefferys prior and two reference priors) for model parameters are obtained and their properties are discussed. Moreover, we propose a class of modified reference priors to remedy weaknesses of the usual reference priors and show that the modified reference priors not only have proper posterior distributions but also have probability matching properties for model parameters. Gibbs sampling algorithms for Bayesian inference based on the Jefferys prior and the modified reference priors are studied. Simulations are conducted to compare the objective Bayesian estimates with the maximum likelihood estimates and subjective Bayesian estimates and shows better performance of the objective method than the other two estimates especially for the case of small sample size. Finally, two real data examples are analyzed for illustration.