A Bayes method for a monotone hazard rate via \(S\)-paths. (English) Zbl 1092.62035

Ho, Man-Wai

Ann. Stat. 34, No. 2, 820-836 (2006).

Summary: A class of random hazard rates, which is defined as a mixture of an indicator kernel convolved 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 of the estimator is proved to be a Rao-Blackwellization of an existing partition characterization or partition-sum estimator. This accentuates the importance of \(S\)-paths 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 characterizations also exist 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.

MSC:

62F15	Bayesian inference
62N02	Estimation in survival analysis and censored data
62G05	Nonparametric estimation

Keywords:

Completely random measure; weighted gamma process; random partition; Rao-Blackwellization; Markov chain Monte Carlo; proportional hazard model; Gibbs sampler

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