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Statistica Sinica 14(2004), 1127-1146





BAYESIAN NONPARAMETRIC SURVIVAL ANALYSIS

VIA LÉVY DRIVEN MARKOV PROCESSES


Luis E. Nieto-Barajas and Stephen G. Walker


ITAM, Mexico and University of Kent, UK


Abstract: In this paper we present and investigate a new class of nonparametric priors for modelling a cumulative distribution function. We take $F(t)=1-\exp\{-Z(t)\}$, where $Z(t)=\int_0^tx(s)\,\d s$ is continuous and $x(\cdot)$ is a Markov process. This is in contrast to the widely used class of neutral to the right priors (Doksum (1974)) for which $Z(\cdot)$ is discrete and has independent increments. The Markov process allows the modelling of trends in $Z(\cdot)$, 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.



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