Nonparametric Bayesian Analysis of Hazard Rate Functions using the Gamma Process Prior

When failure time data are modelled using an inhomogeneous Poisson process, it is necessary to model the underlying hazard rate function lambda(t). The most common approaches to the problem either select some parametric form for lambda(t), or alternatively - conditional on some collected data set - approximate it using the non-parametric Kaplan-Meier estimator. In this paper we present simulation and inference for a non-parametric hazard rate function drawn from a Gamma Process Prior. We use a gamma-scaled Dirichlet Process prior to implement the Gamma Process prior, and construct a Markov Chain Monte Carlo sampler to carry out inference. We demonstrate the methodology with the simulation of a process with an increasing failure rate.