Posterior consistency in conditional distribution estimation

JOURNAL OF MULTIVARIATE ANALYSIS

卷:116

Article

Pati, Debdeep¹  Dunson, David B.²  Tokdar, Surya T.² 

[1] Florida State Univ, Dept Stat, Tallahassee, FL 32306 USA

[2] Duke Univ, Dept Stat Sci, Durham, NC 27706 USA

关键词: Asymptotics;    Bayesian nonparametrics;    Density regression;    Dependent Dirichlet process;    Large support;    Probit stick-breaking process;   

DOI  :  10.1016/j.jmva.2013.01.011

来源: Elsevier

【 摘 要 】

A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. Defining various topologies on the space of conditional distributions, we provide sufficient conditions for posterior consistency focusing on a broad class of priors formulated as predictor-dependent mixtures of Gaussian kernels. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stick-breaking process mixtures in which the stick-breaking lengths are monotone, differentiable functions of a continuous stochastic process. We also provide a set of sufficient conditions for the case where stick-breaking lengths are predictor independent, such as those arising from a fixed Dirichlet process prior. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free