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   -> Volume 5, Issue 1

Preprint: Multiple Shrinkage and Subset Selection in Wavelets
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Brani Vidakovic (brani@isds.Duke.EDU)

PostPosted: Tue Dec 03, 2002 4:15 pm    
Subject: Preprint: Multiple Shrinkage and Subset Selection in Wavelets
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Preprint: Multiple Shrinkage and Subset Selection in Wavelets

Preprint available at

Multiple Shrinkage and Subset Selection in Wavelets
By Merlise Clyde, Giovanni Parmigiani, and Brani Vidakovic

Abstract. This paper discusses Bayesian methods for multiple
shrinkage estimation in wavelets. Wavelets are used in applications
for data compression, via dimension reduction, and for denoising, via
shrinkage of the coefficients. In both areas, there is need for
systematic guidance in the choice of subsets, and for assessment and
incorporation of the uncertainty associated with the selection
process. This motivates looking at a formal probabilistic treatment
of uncertainty in the selection of subsets of basis elements.

We do this using a Bayesian hierarchical model, assigning a
probability distribution to the space of subsets of basis elements.
This defines a multiple shrinkage estimator for the wavelet
coefficients that is based on subset mixing. We show how the induced
shrinkage rule can mimic many standard thresholding policies. In
addition, the subset mixing shrinkage paradigm gives an efficient way
of incorporating prior information about the problem. The degree of
shrinkage can be calibrated based on a number of prior hyperparamters,
whose specification is discussed in detail.

One drawback is the higher computational burden, compared to many
competing estimators. We discuss fast computational implementations.
In particular, we consider easy-to-compute analytic approximations as
well as importance sampling and MCMC methods. We illustrate our
approach with an application.
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