The Annals of Statistics
- Ann. Statist.
- Volume 44, Number 1 (2016), 318-345.
Rate exact Bayesian adaptation with modified block priors
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.
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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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
- 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.