论文标题
关于普通波兰空间的依赖的迪里奇过程
On Dependent Dirichlet Processes for General Polish Spaces
论文作者
论文摘要
我们研究了基于DIRICHLET过程的模型，用于一组依赖于预测变量的概率分布，其中域和预测空间是一般的波兰空间。我们将最初在欧几里得空间构建的依赖性迪里奇过程的定义推广到更通用的波兰空间。我们提供了足够的条件，在这些条件下，依赖的迪里奇过程在连续性（弱和强），关联结构和支持（在不同的拓扑结构下）具有吸引人的特性。我们还提供了足够的条件，在这些条件下，依赖的迪里奇过程引起的混合模型在I.I.D.下具有较强的连续性，关联结构，支持和弱一致性具有吸引人的特性。响应和预测因子的采样。结果可以很容易地扩展到更普遍的破坏摇杆过程。
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.
