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.