On dependent Dirichlet processes for general Polish spaces

We study Dirichlet process-based models for sets of predictor- dependent probability distributions, where the domain and predictor space are general Polish spaces. We generalize the definition of dependent Dirichlet processes, originally constructed on Euclidean spaces, to more general Polish spaces. We provide sufficient conditions under which dependent Dirichlet processes and dependent Dirichlet process mixture models have appealing properties regarding continuity (weak and strong), association structure, and support (under different topologies). The results can be easily extended to more general dependent stick -breaking processes.