Larger posterior mode wavelet thresholding and applications

Abstract

This paper explores the thresholding rules induced by a variation of the Bayesian MAP principle. The MAP rules are Bayes actions that maximize the posterior. The proposed rule is thresholding and always picks the mode of the posterior larger in absolute value, thus the name LPM. We demonstrate that the introduced shrinkage performs comparably to several popular shrinkage techniques. The exact risk properties of the thresholding rule are explored, as well. We provide extensive simulational analysis and apply the proposed methodology to real-life experimental data coming from the field of atomic force microscopy.