A Bayes Method for a Monotone Hazard Rate via S-paths 1,2

A class of random hazard rates, that is defined as a mixture of an indicator kernel convoluted with a completely random measure, is of interest. We provide an explicit characterization of the posterior distribution of this mixture hazard rate model via a finite mixture of S-paths. A closed and tractable Bayes estimator for the hazard rate is derived to be a finite sum over S-paths. The path characterization or the estimator is proved to be a Rao-Blackwellization of an existing partition characterization or partition-sum estimator. This accentuates the importance of S-path in Bayesian modeling of monotone hazard rates. An efficient Markov chain Monte Carlo (MCMC) method is proposed to approximate this class of estimates. It is shown that S-path characterization also exists in modeling with covariates by a proportional hazard model, and the proposed algorithm again applies. Numerical results of the method are given to demonstrate its practicality and effectiveness. This research was in part supported by National University of Singapore research grant R-155-000-047-112 and Hong Kong RGC Competitive Earmarked Research Grant HKUST6159/02P. 2 AMS 2000 subject classifications. Primary 62G05; secondary 62F15.