# 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.

- Author
- Bernard W. Silverman
- Date of publication
- 2012-10-29 08:57:00
- Maintainer
- Ludger Evers <ludger@stats.gla.ac.uk>
- License
- GPL (>= 2)
- Version
- 1.3.2

## Man pages

- beta.cauchy
- Function beta for the quasi-Cauchy prior
- beta.cauchy
- Function beta for the quasi-Cauchy prior
- beta.laplace
- Function beta for the Laplace prior
- beta.laplace
- Function beta for the Laplace prior
- ebayesthresh
- Empirical Bayes thresholding on a sequence
- ebayesthresh
- Empirical Bayes thresholding on a sequence
- ebayesthresh.wavelet
- Empirical Bayes thresholding on the levels of a wavelet...
- ebayesthresh.wavelet
- Empirical Bayes thresholding on the levels of a wavelet...
- isotone
- Weighted least squares monotone regression
- postmean
- Posterior mean estimator
- postmean
- Posterior mean estimator
- postmed
- Posterior median estimator
- postmed
- Posterior median estimator
- tfromw
- Find threshold from mixing weight
- tfromw
- Find threshold from mixing weight
- tfromx
- Find threshold from data
- tfromx
- Find threshold from data
- threshld
- Threshold data with hard or soft thresholding
- threshld
- Threshold data with hard or soft thresholding
- vecbinsolv
- Solve systems of nonlinear equations based on a monotonic...
- vecbinsolv
- Solve systems of nonlinear equations based on a monotonic...
- wandafromx
- Find weight and scale factor from data if Laplace prior is...
- wandafromx
- Find weight and scale factor from data if Laplace prior is...
- wfromt
- Mixing weight from posterior median threshold
- wfromt
- Mixing weight from posterior median threshold
- wfromx
- Find Empirical Bayes weight from data
- wfromx
- Find Empirical Bayes weight from data
- wmonfromx
- Find monotone Empirical Bayes weights from data
- wmonfromx
- Find monotone Empirical Bayes weights from data
- zetafromx
- Estimation of a parameter in the prior weight sequence in the...
- zetafromx
- Estimation of a parameter in the prior weight sequence in the...

## Files in this package

EbayesThresh |

EbayesThresh/NAMESPACE |

EbayesThresh/man |

EbayesThresh/man/tfromw.Rd |

EbayesThresh/man/threshld.Rd |

EbayesThresh/man/isotone.Rd |

EbayesThresh/man/ebayesthresh.wavelet.Rd |

EbayesThresh/man/zetafromx.Rd |

EbayesThresh/man/beta.laplace.Rd |

EbayesThresh/man/beta.cauchy.Rd |

EbayesThresh/man/wmonfromx.Rd |

EbayesThresh/man/postmed.Rd |

EbayesThresh/man/wfromx.Rd |

EbayesThresh/man/postmean.Rd |

EbayesThresh/man/wfromt.Rd |

EbayesThresh/man/wandafromx.Rd |

EbayesThresh/man/tfromx.Rd |

EbayesThresh/man/ebayesthresh.Rd |

EbayesThresh/man/vecbinsolv.Rd |

EbayesThresh/DESCRIPTION |

EbayesThresh/MD5 |

EbayesThresh/R |

EbayesThresh/R/beta.cauchy.R |

EbayesThresh/R/postmean.laplace.R |

EbayesThresh/R/cauchy.medzero.R |

EbayesThresh/R/vecbinsolv.R |

EbayesThresh/R/beta.laplace.R |

EbayesThresh/R/threshld.R |

EbayesThresh/R/postmean.R |

EbayesThresh/R/zetafromx.R |

EbayesThresh/R/ebayesthresh.wavelet.R |

EbayesThresh/R/laplace.threshzero.R |

EbayesThresh/R/tfromw.R |

EbayesThresh/R/wfromx.R |

EbayesThresh/R/wfromt.R |

EbayesThresh/R/ebayesthresh.wavelet.dwt.R |

EbayesThresh/R/postmed.R |

EbayesThresh/R/ebayesthresh.R |

EbayesThresh/R/negloglik.laplace.R |

EbayesThresh/R/postmed.laplace.R |

EbayesThresh/R/wmonfromx.R |

EbayesThresh/R/postmean.cauchy.R |

EbayesThresh/R/wandafromx.R |

EbayesThresh/R/postmed.cauchy.R |

EbayesThresh/R/isotone.R |

EbayesThresh/R/cauchy.threshzero.R |

EbayesThresh/R/ebayesthresh.wavelet.splus.R |

EbayesThresh/R/tfromx.R |

EbayesThresh/R/ebayesthresh.wavelet.wd.R |