Abstract
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.
Funding Statement
A. Iturriaga was supported by “Becas de Doctorado Nacional de CONICYT” and by Agencia Nacional de Investigación y Desarrollo (ANID) through the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) grant No 1200221.
C. A. Sing Long was supported by Agencia Nacional de Investigación y Desarrollo (ANID) through the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) grant No 1211643 and through grant NCN17 059 from Millennium Science Initiative Program, Millennium Nucleus Center for the Discovery of Structures in Complex Data (MIDAS).
A. Jara’s work was supported by Agencia Nacional de Investigación y Desarrollo (ANID) through the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) grant No 1220907 and through grant NCN17 059 from Millennium Science Initiative Program, Millennium Nucleus Center for the Discovery of Structures in Complex Data (MIDAS).
Acknowledgments
The authors would like to thank the anonymous referees for their constructive comments that improved the quality of this paper. The authors are grateful for helpful discussions with Prof. Judith Rousseau.
Citation
Andrés Iturriaga. Carlos A. Sing Long. Alejandro Jara. "On dependent Dirichlet processes for general Polish spaces." Electron. J. Statist. 18 (1) 2064 - 2134, 2024. https://doi.org/10.1214/24-EJS2245
Information
