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Nonparametric Bayesian inference from right censored survival data, using the Gibbs sampler. (English) Zbl 0823.62030

Summary: Consider simple right censored survival data with a common unknown hazard rate. The hazard rate is here modelled nonparametrically, as a jump process having a martingale structure with respect to the prior distribution. For an evaluation of posterior probabilities, given the data, sample paths of the hazard rate are generated from the posterior distribution by using a dynamic version of the Gibbs sampler. The algorithm is described in detail. It is also shown how, by slightly modifying the algorithm, the procedure can be altered to correspond to a constrained estimation problem where the hazard rate is known to be increasing (or decreasing). The methods are illustrated by simulation examples.

MSC:

62G07 Density estimation
62G05 Nonparametric estimation
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