Bayesian Inference and Prediction Analysis of the Power Law Process Based on a Gamma Prior Distribution

Abstract

Under a Gamma prior distribution, the importance sampling (IS) technique is applied to the Bayesian analysis of the Power Law Process (PLP). Samples of important parameters in the PLP are obtained from IS. Based on these samples, not only the posterior analyses of parameters and some functions of the parameter in the PLP can be performed conveniently, but also single-sample and two-sample predictions are constructed easily by the transformation formula of double integral. The sensitivity of the posterior mean of the parameter functions in the PLP is studied with respect to the prior moments in the Gamma prior distribution, and it can guide the selections of the prior moments. After some numerical experiments illustrate the rationality and feasibility of the proposed methods, an engineering example demonstrates its application.

Keywords:

• Bayesian inference
• Importance sampling
• Prediction analysis
• Power Law Process
• Reliability growth

Mathematics Subject Classification:

• 62F15
• 62M20
• 62N05

Acknowledgments

This work was supported by National Natural Science Foundation of China (NSFC50875213), Aeronautical Science Foundation of China (2007ZA53012), National High-tech Research and Development Program (2007AA04Z401), and Important National Science & Technology Specific Projects (2009ZX04014-015-03).