Rate exact Bayesian adaptation with modified block priors
arXiv:1312.3937 · doi:10.1214/15-AOS1368
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.
Published at http://dx.doi.org/10.1214/15-AOS1368 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (7)
- Convergence rates of posterior distributions for noniid observations
- Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth
- Bayesian inference with rescaled Gaussian process priors
- On adaptive posterior concentration rates
- Adaptive nonparametric Bayesian inference using location-scale mixture priors
- Convergence rates for Bayesian density estimation of infinite-dimensional exponential families
- Nonparametric Bayesian model selection and averaging