Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression

In the last decade, many authors studied asymptotic optimality of Bayesian wavelet estimators such as the posterior median and the posterior mean. In this paper, we consider contraction rates of the posterior distribution in Bayesian wavelet regression in L2/l2 neighborhood of the true parameter, wh...

Full description

Saved in:
Bibliographic Details
Main Author: Lian, Heng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
Online Access:https://hdl.handle.net/10356/96486
http://hdl.handle.net/10220/18070
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-96486
record_format dspace
spelling sg-ntu-dr.10356-964862020-03-07T12:34:42Z Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression Lian, Heng School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics In the last decade, many authors studied asymptotic optimality of Bayesian wavelet estimators such as the posterior median and the posterior mean. In this paper, we consider contraction rates of the posterior distribution in Bayesian wavelet regression in L2/l2 neighborhood of the true parameter, which lies in some Besov space. Using the common spike-and-slab-type of prior with a point mass at zero mixed with a Gaussian distribution, we show that near-optimal rates (that is optimal up to extra logarithmic terms) can be obtained. However, to achieve this, we require that the ratio between the log-variance of the Gaussian prior component and the resolution level is not constant over different resolution levels. Furthermore, we show that by putting a hyperprior on this ratio, the approach is adaptive in that knowledge of the value of the smoothness parameter is no longer necessary. We also discuss possible extensions to other priors such as the sieve prior. 2013-12-05T02:57:03Z 2019-12-06T19:31:21Z 2013-12-05T02:57:03Z 2019-12-06T19:31:21Z 2013 2013 Journal Article Lian, H. (2013). Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression. Journal of statistical planning and inference, in press. 0378-3758 https://hdl.handle.net/10356/96486 http://hdl.handle.net/10220/18070 10.1016/j.jspi.2013.09.002 en Journal of statistical planning and inference
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Applied mathematics
spellingShingle DRNTU::Science::Mathematics::Applied mathematics
Lian, Heng
Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
description In the last decade, many authors studied asymptotic optimality of Bayesian wavelet estimators such as the posterior median and the posterior mean. In this paper, we consider contraction rates of the posterior distribution in Bayesian wavelet regression in L2/l2 neighborhood of the true parameter, which lies in some Besov space. Using the common spike-and-slab-type of prior with a point mass at zero mixed with a Gaussian distribution, we show that near-optimal rates (that is optimal up to extra logarithmic terms) can be obtained. However, to achieve this, we require that the ratio between the log-variance of the Gaussian prior component and the resolution level is not constant over different resolution levels. Furthermore, we show that by putting a hyperprior on this ratio, the approach is adaptive in that knowledge of the value of the smoothness parameter is no longer necessary. We also discuss possible extensions to other priors such as the sieve prior.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Lian, Heng
format Article
author Lian, Heng
author_sort Lian, Heng
title Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
title_short Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
title_full Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
title_fullStr Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
title_full_unstemmed Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
title_sort adaptive rates of contraction of posterior distributions in bayesian wavelet regression
publishDate 2013
url https://hdl.handle.net/10356/96486
http://hdl.handle.net/10220/18070
_version_ 1681036851733856256