Monte Carlo Methods for Approximating a Posterior Hazard Rate Process

P.W. Laud, A.F.M. Smith, P. Damien
Medical College of Wisconsin, Imperial College, Duke University, Kimberly-Clark Corp.

Nov 30 1993

In the context of Bayesian nonparametric statistics, the distribution of a stochastic process serves a a prior over the class of functions indexed by its sample paths. Dykstra and Laud (1981) defined a stochastic process whose sample paths can be used to index monotone hazard rates. Although they gave a mathematical description of the corresponding posterior process, numerical evaluations of useful posterior summaries were not feasible for realistic sample sizes. Here we show how a full Bayesian posterior computation is made possible by novel Monte Carlo methods that approximate random increments of the posterior process.


Extended gamma process, hazard rates, latent variables, laplace transform, infinitely divisible distributions


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