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Title: Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression
Authors: Lian, Heng
Keywords: DRNTU::Science::Mathematics::Applied mathematics
Issue Date: 2013
Source: Lian, H. (2013). Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression. Journal of statistical planning and inference, in press.
Series/Report no.: Journal of statistical planning and inference
Abstract: 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.
ISSN: 0378-3758
DOI: 10.1016/j.jspi.2013.09.002
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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