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April 2006 A Bayes method for a monotone hazard rate via S-paths
Man-Wai Ho
Ann. Statist. 34(2): 820-836 (April 2006). DOI: 10.1214/009053606000000047


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.


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Man-Wai Ho. "A Bayes method for a monotone hazard rate via S-paths." Ann. Statist. 34 (2) 820 - 836, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1092.62035
MathSciNet: MR2283394
Digital Object Identifier: 10.1214/009053606000000047

Primary: 62G05
Secondary: 62F15

Keywords: completely random measure , Gibbs sampler , Markov chain Monte Carlo , proportional hazard model , random partition , Rao–Blackwellization , weighted gamma process

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • April 2006
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