ADAPTIVE NONPARAMETRIC BAYESIAN INFERENCE USING LOCATION-SCALE MIXTURE PRIORS

被引：30

作者：

de Jonge, R. ^{[1
]}

van Zanten, J. H. ^{[1
]}

机构：

[1] Eindhoven Univ Technol, Dept Math, NL-5600 MB Eindhoven, Netherlands

来源：

ANNALS OF STATISTICS | 2010年 / 38卷 / 06期

关键词：

Rate of convergence; posterior distribution; adaptation; Bayesian inference; nonparametric regression; kernel mixture priors; POSTERIOR CONVERGENCE-RATES; DIRICHLET MIXTURES; DENSITY-ESTIMATION; GAUSSIAN MEASURES; METRIC ENTROPY; DISTRIBUTIONS; APPROXIMATION; CONSISTENCY; MODELS;

D O I：

10.1214/10-AOS811

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a Gaussian kernel, an inverse gamma bandwidth, and Gaussian mixing weights.

引用

页码：3300 / 3320

页数：21

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