The Annals of Statistics

Rate exact Bayesian adaptation with modified block priors

Chao Gao and Harrison H. Zhou

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1449755965

Digital Object Identifier
doi:10.1214/15-AOS1368

Mathematical Reviews number (MathSciNet)
MR3449770

Zentralblatt MATH identifier
1331.62215

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

Keywords
Bayesian nonparametrics adaptive estimation block prior

Citation

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. https://projecteuclid.org/euclid.aos/1449755965


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References

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.