Are Gibbs-Type Priors the Most Natural Generalization of the Dirichlet Process?
IEEE Trans Pattern Anal Mach Intell
; 37(2): 212-29, 2015 Feb.
Article
en En
| MEDLINE
| ID: mdl-26353237
Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Here we focus on the family of Gibbs-type priors, a recent elegant generalization of the Dirichlet and the Pitman-Yor process priors. These random probability measures share properties that are appealing both from a theoretical and an applied point of view: (i) they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism; (ii) they stand out in terms of mathematical tractability; (iii) they include several interesting special cases besides the Dirichlet and the Pitman-Yor processes. The goal of our paper is to provide a systematic and unified treatment of Gibbs-type priors and highlight their implications for Bayesian nonparametric inference. We deal with their distributional properties, the resulting estimators, frequentist asymptotic validation and the construction of time-dependent versions. Applications, mainly concerning mixture models and species sampling, serve to convey the main ideas. The intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the Dirichlet process.
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1
Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
IEEE Trans Pattern Anal Mach Intell
Asunto de la revista:
INFORMATICA MEDICA
Año:
2015
Tipo del documento:
Article
Pais de publicación:
Estados Unidos