Bayesian Wavelet Shrinkage Strategies: A Review

In this chapter the authors overview recent developments and current status of use of Bayesian paradigm in wavelet shrinkage. The paradigmatic problem where wavelet shrinkage is employed is that of nonparametric regression where data are modeled as observations from an unknown signal contaminated with a Gaussian noise. Bayes rules as general shrinkers provide a formal mechanism to implement shrinkage in the wavelet domain that is model based and adaptive. New developments including dependence models, complex wavelets and MCMC strategies are described. Applications include inductance plethysmography data and curve classification procedure applied in botany. The chapter features an extensive set of references consisting of almost 100 entries.

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