Monte Carlo Methods for Approximating a Posterior Hazard Rate Process

Authors: 
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.

Keywords: 

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

Manuscript: 

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