Bayesian nonparametric survival analysis via Lévy driven Markov processes

Abstract: In this paper we present and investigate a new class of nonparamet-ric priors for modelling a cumulative distribution function. We take F (t) = 1 − exp{−Z(t)}, where Z(t) = ∫ 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 in-crements. We derive posterior distributions and present a full Bayesian analysis