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.
Publié le : 2006-04-14
Classification:
Completely random measure,
weighted gamma process,
random partition,
Rao–Blackwellization,
Markov chain Monte Carlo,
proportional hazard model,
Gibbs sampler,
62G05,
62F15
@article{1151418242,
author = {Ho, Man-Wai},
title = {A Bayes method for a monotone hazard rate via S-paths},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 820-836},
language = {en},
url = {http://dml.mathdoc.fr/item/1151418242}
}
Ho, Man-Wai. A Bayes method for a monotone hazard rate via S-paths. Ann. Statist., Tome 34 (2006) no. 1, pp. 820-836. http://gdmltest.u-ga.fr/item/1151418242/