The Annals of Statistics

A Bayes method for a monotone hazard rate via S-paths

Man-Wai Ho

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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 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-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 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.

Article information

Ann. Statist., Volume 34, Number 2 (2006), 820-836.

First available in Project Euclid: 27 June 2006

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62F15: Bayesian inference

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


Ho, Man-Wai. A Bayes method for a monotone hazard rate via S -paths. Ann. Statist. 34 (2006), no. 2, 820--836. doi:10.1214/009053606000000047.

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