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Bayesian Approach to Wavelet Decomposition and Shrinkage

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Bayesian Inference in Wavelet-Based Models

Part of the book series: Lecture Notes in Statistics ((LNS,volume 141))

Abstract

We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function’s regularity can be incorporated into a prior model for its wavelet coefficients by establishing a relationship between the hyperparameters of the proposed model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relation may be seen as giving insight into the meaning of the Besov space parameters themselves. Furthermore, we consider Bayesian wavelet-based function estimation that gives rise to different types of wavelet shrinkage in non-parametric regression. Finally, we discuss an extension of the proposed Bayesian model by considering random functions generated by an overcomplete wavelet dictionary.

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Authors
  1. Felix Abramovich
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  2. Theofanis Sapatinas
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Editor information

Editors and Affiliations

  1. Institute of Statistics and Decision Sciences, Duke University, Box 90251, Durham, 27708-0251, NC, England

    Peter Müller  & Brani Vidakovic  & 

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Abramovich, F., Sapatinas, T. (1999). Bayesian Approach to Wavelet Decomposition and Shrinkage. In: Müller, P., Vidakovic, B. (eds) Bayesian Inference in Wavelet-Based Models. Lecture Notes in Statistics, vol 141. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0567-8_3

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  • DOI: https://doi.org/10.1007/978-1-4612-0567-8_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98885-6

  • Online ISBN: 978-1-4612-0567-8

  • eBook Packages: Springer Book Archive

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