Statistica Sinica 4(1994), 505-524

NONPARAMETRIC BAYESIAN INFERENCE FROM

RIGHT CENSORED SURVIVAL DATA, USING

THE GIBBS SAMPLER

Elja Arjas and Dario Gasbarra

University of Oulu

Abstract: 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.

Key words and phrases: Hazard rate, Markov chain Monte Carlo integration, posterior distribution, predictive distribution, Bayesian smoothing, constrained estimation.