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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