beta.cauchy

<p>Given a value or vector \(x\) of values, find the value(s) of the
function \(\beta(x)=g(x)/\phi(x) - 1\),
where \(g\) is the convolution of the quasi-Cauchy with the normal
density \(\phi(x)\).</p>

nonparametric

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.

Peter Carbonetto

EbayesThresh

Empirical Bayes Thresholding and Related Methods

Bernard W. Silverman

Ludger Evers

Kan Xu

Matthew Stephens

beta.cauchy function

Function beta for the quasi-Cauchy prior — beta.cauchy

Function beta for the quasi-Cauchy prior

beta.cauchy: Function beta for the quasi-Cauchy prior

Description

Usage

Arguments

Value

References

See Also

Examples