Empirical Bayes Thresholding and Related Methods
Weighted least squares monotone regression
Function beta for the quasi-Cauchy prior
Posterior mean estimator
Function beta for the Laplace prior
Empirical Bayes thresholding on a sequence
Empirical Bayes thresholding on the levels of a wavelet transform.
Posterior median estimator
Find threshold from mixing weight
Find thresholds from data
Threshold data with hard or soft thresholding
Solve systems of nonlinear equations based on a monotonic function
Find weight and scale factor from data if Laplace prior is used.
Mixing weight from posterior median threshold
Find Empirical Bayes weight from data
Find monotone Empirical Bayes weights from data.
Estimation of a parameter in the prior weight sequence in the EbayesTh...
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.
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