Flexible clustering via hidden hierarchical Dirichlet priors

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular nonparametric model clustering probability distributions is nested Dirichlet process, which however has drawback of grouping in a single cluster when ties are observed samples. With goal achieving flexible and effective method both observations, we investigate prior that arises as composition two discrete random structures derive closed-form expression induced distribution partition, fundamental tool regulating behavior model. On one hand, this allows gain deeper insight into theoretical properties and, on other it yields an MCMC algorithm evaluating inferences interest. Moreover, limitations working more than populations consequently, devise alternative efficient sampling scheme, by-product, testing homogeneity between populations. Finally, perform comparison process provide illustrative examples synthetic real data.