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 have appealing properties regarding continuity (weak and strong), association structure, and support (under different topologies). We also provide sufficient conditions under which mixture models induced by dependent Dirichlet processes have appealing properties regarding strong continuity, association structure, support, and weak consistency under i.i.d. sampling of both responses and predictors. The results can be easily extended to more general dependent stick-breaking processes.

翻译：我们研究了Drichlet的预测或依赖概率分布的成套模型,其中域和预测空间为波兰一般空间;我们将最初在欧几里德空间建造的附属迪里赫莱工艺的定义推广到波兰较为普遍的空间;我们提供了足够条件,使独立的迪里赫莱工艺在连续性(弱和强)、联系结构和支持(不同地层)方面具有吸引力;我们还提供了足够条件,使依赖迪里特工艺引发的混合模型具有很强的连续性、联系结构、支持性以及根据i.d.抽样反应和预测器的不一致性。结果可以很容易推广到更普遍的依赖性粘合工艺。