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

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