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 coeecients 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 insig...

New challenges have arisen with the development of large marker panels for livestock species. Models easily become overparameterized when all available markers are included. Solutions have led to the development of shrinkage or regularization techniques. The objective of this study was the application and comparison of Bayesian LASSO (B-L), thick-tailed (Student-t), and semiparametric multiple ...

The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical, have been obtained. Here we trace some of the developments in confidence set estimation.

Wavelet shrinkage is a non parametric technique used in curve estimation. The idea is to shrink wavelet coefficients towards zero using statistical methods. More specifically, a threshold value is chosen and wavelet coefficients whose absolute values exceed that threshold are kept while others are removed. This has the effect of both reducing the noise contribution and compressing the original ...

A problem of classification of local field potentials (LFPs), recorded from the prefrontal cortex of a macaque monkey, is considered. An adult macaque monkey is trained to perform a memory based saccade. The objective is to decode the eye movement goals from the LFP collected during a memory period. The LFP classification problem is modeled as that of classification of smooth functions embedded...

The denoising of a natural image corrupted by additive white Gaussian noise (AWGN) is a classical problem in the signal processing community. The corruption of an image by noise is common during its acquisition or transmission. The aim of denoising is to remove the noise while keeping the signal featuresas much as possible. Traditional algorithms, such as the standard median (SM) filter and mea...

and Michael Lavine for useful discussions and the editor, associate editor, and the two anonymous referees for insightful comments. 2 Wavelet shrinkage, the method proposed by the seminal work of Donoho and Johnstone is a disarmingly simple and eecient way of denoising data. Shrinking wavelet coeecients was proposed from several optimality criteria. In this article a wavelet shrinkage by cohere...

For the ill-posed linear inverse problem, we propose a hybrid regularization model, which possesses characters of Tikhonov and TV to some extent. Through transformation, is reformulated as an equivalent minimization problem. To solve present two modified iterative shrinkage-thresholding algorithms (MISTA) based on fast algorithm (FISTA) shrinkagethresholding (ISTA). The numerical experiments ar...