Paper No. 09-05

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JE Griffin and MFJ Steel

Time-Dependent Stick-Breaking Processes

Abstract: This paper considers the problem of defining a time-dependent nonparametric prior. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals have interesting interpretations that are further investigated. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the stick-breaking process form increasing sequences. We derive a P´olya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. The results section shows the relative performance of the two MCMC schemes for the Dirichlet process case and contains three real data examples.