Wavelet thresholding via a Bayesian approach

Abramovich, Felix and Sapatinas, Theofanis and Silverman, B.W. (1998) Wavelet thresholding via a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60 . pp. 725-49. ISSN 1369-7412. (doi:https://doi.org/10.1111/1467-9868.00151) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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 that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to elicit; with this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study.

Item Type: Article
Uncontrolled keywords: adaptive estimation; anaesthetics; Bayes model; Besov spaces; nonparametric regression; thresholding; wavelet transform
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: I. Ghose
Date Deposited: 05 Apr 2009 07:50 UTC
Last Modified: 09 May 2014 14:10 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/17534 (The current URI for this page, for reference purposes)
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