EbayesThresh: Empirical Bayes Thresholding and Related Methods
This package carries out Empirical Bayes thresholding
using the methods developed by I. M. Johnstone and B. W.
Silverman. The basic problem is to estimate a mean vector given
a vector of observations of the mean vector plus white noise,
taking advantage of possible sparsity in the mean vector.
Within a Bayesian formulation, the elements of the mean vector
are modelled as having, independently, a distribution that is a
mixture of an atom of probability at zero and a suitable
heavy-tailed distribution. The mixing parameter can be
estimated by a marginal maximum likelihood approach. This
leads to an adaptive thresholding approach on the original
data. Extensions of the basic method, in particular to wavelet
thresholding, are also implemented within the package.