期刊
STATISTICAL SCIENCE
卷 37, 期 1, 页码 24-41出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/20-STS819
关键词
Related random probability distributions; Bayesian nonparametrics; nonparametric regression; quantile regression
资金
- ANID-Millennium Science Initiative Program [NCN17_059]
- Fondecyt [1180640, 1180034]
- National Science Foundation [DMS-1952679]
- U.S. National Cancer Institute [R01 CA132897]
Standard regression approaches assume finite characteristics of the response distribution vary with predictors, but in reality, responses often change in ways that cannot be represented by a finite dimensional form. This has led to the study of fully nonparametric regression models to tackle the general problem. Various Bayesian approaches, such as dependent Dirichlet processes, have been developed to define probability models where the response distribution can vary flexibly with predictors.
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate to assume a location/scale representation, where the error distribution has unchanging shape over the predictor space. In fact, it often happens in applied research that the distribution of responses under study changes with predictors in ways that cannot be reasonably represented by a finite dimensional functional form. This can seriously affect the answers to the scientific questions of interest, and therefore more general approaches are indeed needed. This gives rise to the study of fully nonparametric regression models. We review some of the main Bayesian approaches that have been employed to define probability models where the complete response distribution may vary flexibly with predictors. We focus on developments based on modifications of the Dirichlet process, historically termed dependent Dirichlet processes, and some of the extensions that have been proposed to tackle this general problem using nonparametric approaches.
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