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A Bayes Method for a Monotone Hazard Rate via S-Paths

Man-Wai Ho
The Annals of Statistics
Vol. 34, No. 2 (Apr., 2006), pp. 820-836
Stable URL: http://www.jstor.org/stable/25463438
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Bayes Method for a Monotone Hazard Rate via S-Paths
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Abstract

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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