Monte Carlo Methods for Approximating a Posterior Hazard Rate Process
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