The Annals of Statistics

Rate exact Bayesian adaptation with modified block priors

Chao Gao and Harrison H. Zhou

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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.

Article information

Ann. Statist. Volume 44, Number 1 (2016), 318-345.

Received: August 2014
Revised: July 2015
First available in Project Euclid: 10 December 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G20: Asymptotic properties

Bayesian nonparametrics adaptive estimation block prior


Gao, Chao; Zhou, Harrison H. Rate exact Bayesian adaptation with modified block priors. Ann. Statist. 44 (2016), no. 1, 318--345. doi:10.1214/15-AOS1368.

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Supplemental materials

  • Supplement to “Rate exact Bayesian adaptation with modified block priors”. The supplementary material [Gao and Zhou (2015)] contains the remaining proofs and numerical studies of the block prior.