Bayesian nonparametric survival analysis via Levy driven Markov processes

In this paper we present and investigate a new class of non-parametric priors for modelling a cumulative distribution function. We take F(t) = 1 - exp{-Z(t)}; where Z(t) = integral(t)/(0) x(s) ds is continuous and x((.)) is a Markov process. This is in contrast to the widely used class of neutral to the right priors (Doksum (1974)) for which Z(.) is discrete and has independent increments. The Markov process allows the modelling of trends in Z(.), not possible with independent increments. We derive posterior distributions and present a, full Bayesian analysis.