Model Selection For Bounded Transformed Gamma Processes: Bayesian Approach

The bounded transformed gamma process (BTGP) was recently proposed to describe degradation phenomena where the degradation growth is monotonic increasing and intrinsically bounded above. The BGTP is ruled by two monotone increasing functions, namely age and bounded state functions, whose functional form influences the behavior of the degradation model. In this paper, a Bayesian model selection procedure, based on the Bayes factor, is introduced to select the functional form of the bounded state function maximizing the marginal likelihood and thus providing the best fit to the available degradation data among suitable alternatives. The Bayesian model selection procedure involves prior information on the upper bound of the degradation phenomenon and on the behavior of the mean degradation function, and is performed by adopting some Markov Chain Monte Carlo procedures. The proposed approach is applied to a set of real data consisting of the wear measurements of the liners of an 8-cylinder Diesel engine for marine propulsion.