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We study Dirichlet process-based models for sets of predictor-dependentprobability distributions, where the domain and predictor space are generalPolish spaces. We generalize the definition of dependent Dirichlet processes,originally constructed on Euclidean spaces, to more general Polish spaces. Weprovide sufficient conditions under which dependent Dirichlet processes haveappealing properties regarding continuity (weak and strong), associationstructure, and support (under different topologies). We also provide sufficientconditions under which mixture models induced by dependent Dirichlet processeshave appealing properties regarding strong continuity, association structure,support, and weak consistency under i.i.d. sampling of both responses andpredictors. The results can be easily extended to more general dependentstick-breaking processes.

On Dependent Dirichlet Processes for General Polish Spaces