Duration Model Bayesian Semi-parametric Approach

In this chapter, we use the semi-parametric Bayesian approach in the proportional hazard model generalizing the results of Kalbfleisch (Journal of the Royal Statistical Society. Series B (Methodological), 40(2), 214–221 (1978)). Basically we consider the parameter of interest as random and assume a nonrestrictive hypothesis that the functional nuisance parameter is purely random. We give some results on Gamma and Dirichlet distributions laws. In the specific case of Gamma process, we try to give some interpretation of classical results using Bayesian semi-parametric approach. As for the estimation of the nuisance parameter, we simply use an iterative expectation rule and a recurrence approach.