Abstract: In this paper we present and investigate a new class of nonparametric priors for modelling a cumulative distribution function. We take , where is continuous and is a Markov process. This is in contrast to the widely used class of neutral to the right priors (Doksum (1974)) for which is discrete and has independent increments. The Markov process allows the modelling of trends in , not possible with independent increments. We derive posterior distributions and present a full Bayesian analysis.
Key words and phrases: Bayes nonparametrics, consistency, Lévy process, gamma process, Markov process, stationary process, Lévy driven Markov process.