Modelling heterogeneity with and without the Dirichlet process (Q137459)

Nonparametric Bayesian hierarchical models construction techniques based on Dirichlet process priors (DP) and the technique of Dirichlet-multinomial allocation models (DMA) are considered. It is noted that the DP model is a limit of DMA when the number of components tends to \(\infty\) while the total of Dirichlet parameters remains fixed. As an example, the problem of Bayesian nonparametric density estimation is considered. The authors describe Markov chain Monte Carlo algorithms of samplers generation and compare their performance via simulation studies.