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Multivariate Bayes Wavelet shrinkage and applications

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  • Gabriel Huerta

Abstract

In recent years, wavelet shrinkage has become a very appealing method for data de-noising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented.

Suggested Citation

  • Gabriel Huerta, 2005. "Multivariate Bayes Wavelet shrinkage and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(5), pages 529-542.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:5:p:529-542
    DOI: 10.1080/02664760500079662
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    References listed on IDEAS

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    1. Merlise Clyde & Edward I. George, 2000. "Flexible empirical Bayes estimation for wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 681-698.
    2. M. Vannucci & F. Corradi, 1999. "Covariance structure of wavelet coefficients: theory and models in a Bayesian perspective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 971-986.
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    Cited by:

    1. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.

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