Bayesian prediction analysis of the intensity of the power law process based on G-M method and importance sampling technique

Under various reasonable noninformative priors, the hybrid of Gibbs sampling and Metropolis- Hastings algorithm, and importance sampling technique have been employed to Bayesian prediction of the intensity of the power law process. Bayesian analysis of the intensity of the power law process is facilitated, and then Bayes estimates and credible intervals of the intensity and functions of the intensity of the power law process can be easily obtained. The given prediction methods are exploited to predict not only the future intensity but also the current intensity. After results from a numerical simulation example with real value illustrate the feasibility, rationality and validity of presented methods, a real example is given. As for selection of noninformative priors, this paper provides some advices.