By taking the governing measure of a Dirichlet process as essentially the realization of a Dirichlet process itself, a hierarchical Dirichlet process emerges. This distribution enables the Bayesian treatment of two level hierarchical random effects models, with results paralleling those of Ferguson (1973).

6.

The model is a DP mixture of normals for related random probability measures Hj . Each random measure is assumed to arise as a mixture Hj = F0 + (1 − )Fj of one common distribution F0 and a distribution Fj that is specific to the j-th submodel. See Mueller, Quintana and Rosner (2004) for details of the model. In summary, the implemented model is as follows. Without loss of generality we assume ...