A mixture of beta–Dirichlet processes prior for Bayesian analysis of event history data

Abstract

In this paper, we propose a mixture of beta-Dirichlet processes as a nonparametric prior for the cumulative intensity functions of a Markov process. This family of priors is a natural extension of a mixture of Dirichlet processes or a mixture of beta processes which are devised to compromise advantages of parametric and nonparametric approaches. They give most of their prior mass to the small neighborhood of a specific parametric model. We show that a mixture of beta Dirichlet processes prior is conjugate with Markov processes. Formulas for computing the posterior distribution are derived. Finally, results of analyzing credit history data are given. (C) 2012 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.