Modelling heterogeneity with and without the Dirichlet process

by Peter Green (Bristol, UK) and Sylvia Richardson (INSERM, France).
The relationships between Dirichlet process (DP) based models and allocation models based on exchangeable distributions are investigated. It is shown that DP partition distribution is a limiting case of a Dirichlet-Multinomial allocation model. Exploiting this connection in a Bayesian paradigm, a new MCMC sampler for general DP based models is introduced which uses split/merge moves in a reversible jump framework. Performance of this new sampler relative to that of traditional samplers for DP processes is then explored in the context of univariate mixture models. Statistical comparisons between the posterior performance of DP and allocation models are made in the same context.
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