Multiple shrinkage and subset selection in wavelets

Merlise Clyde, Giovanni Parmigiani, Brani Vidakovic

Research output: Contribution to journalArticlepeer-review

Abstract

This paper discusses Bayesian methods for multiple shrinkage estimation in wavelets. Wavelets are used in applications for data denoising, via shrinkage of the coefficients towards zero, and for data compression, by shrinkage and setting small coefficients to zero. We approach wavelet shrinkage by using Bayesian hierarchical models, assigning a positive prior probability to the wavelet coefficients being zero. The resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns. We discuss fast computational implementations, with a focus on easy-to-compute analytic approximations as well as importance sampling and Markov chain Monte Carlo methods. Multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions. We demonstrate this in simulated test examples, comparing various implementations of multiple shrinkage to commonly-used shrinkage rules. Finally, we illustrate our approach with an application to the so-called 'glint' data. Gibbs sampling; Importance sampling; Model averaging.

Original languageEnglish (US)
Pages (from-to)391-401
Number of pages11
JournalBiometrika
Volume85
Issue number2
StatePublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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