Modelling heterogeneity with and without the Dirichlet process

We investigate the relationships between Dirichlet process (DP) based model s and allocation models for a variable number of components, based on excha ngeable distributions. It is shown that the DP partition distribution is a Limiting case of a Dirichlet-multinomial allocation model, Comparisons of p osterior performance of DP and allocation models are made in the Bayesian p aradigm and illustrated in the context of univariate mixture models, It is shown in particular that the unbalancedness of the allocation distribution, present in the prior DP model, persists aposteriori, Exploiting the model connections, 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 some traditional samplers for DP proc esses is teen explored.