RATE EXACT BAYESIAN ADAPTATION WITH MODIFIED BLOCK PRIORS

• 成果类型: Article
• 署名作者: Gao, Chao; Zhou, Harrison H.
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1368
• 发表日期: 2016
• 页码: 318-345
• 关键词: dimensional exponential-families; Posterior Concentration Rates; gaussian white-noise; DENSITY-ESTIMATION; asymptotic equivalence; convergence-rates; Nonparametric Regression; dirichlet mixtures; distributions; inference

摘要

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.