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   -> Volume 5, Issue 10


Preprint: Wavelet Thresholding via a Bayesian Approach
 
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mafs (t.sapatinas@bristol.ac.uk)
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PostPosted: Sat Nov 09, 1996 4:19 pm    
Subject: Preprint: Wavelet Thresholding via a Bayesian Approach
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#1 Preprint: Wavelet Thresholding via a Bayesian Approach

Dear readers,

The following preprint is available:

Authors: Abramovich, F., Sapatinas, T. and Silverman, B.W.

Title: Wavelet Thresholding via a Bayesian Approach

Abstract. We discuss a Bayesian formalism which gives rise to a type
of wavelet threshold estimation in nonparametric regression. A prior
distribution is imposed on the wavelet coefficients of the unknown
response function, designed to capture the sparseness of wavelet
expansion common to most applications. For the prior specified, the
posterior median yields a thresholding procedure. Several examples are
used to illustrate the method, and comparisons are made with other
thresholding methods. We also present an application to a real data
set collected in an anaesthesiological study. Not surprisingly,
incorporating reasonable prior information about the smoothness of the
signal can improve the quality of estimates. Our prior model for the
underlying function can be adjusted to give functions falling in any
specific Besov space. We establish a relation between the
hyperparameters of the prior model and the parameters of those Besov
spaces within which realizations from the prior will fall. This makes
it possible to incorporate prior knowledge about the function's
regularity properties into the prior model for its wavelet
coefficients. It is therefore of interest in its own right as a way of
understanding and demonstrating the meaning of the Besov space
parameters.

This preprint is available at:

http://www.stats.bris.ac.uk/~mafs/bayesthresh_1.ps.gz

Dr. Theofanis Sapatinas, * e-mail: T.Sapatinas@bristol.ac.uk *
Department of Mathematics, | |
Bristol University, * Tel: + (44)-0117-9287980 *
University Walk, | |
Bristol BS8 1TW, * Fax: + (44)-0117-9287999 *
United Kingdom. | |
All times are GMT + 1 Hour
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