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  "Title": "Empirical Bayes Thresholding and Related Methods",
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  "Description": "Empirical Bayes thresholding using the methods developed\nby I. M. Johnstone and B. W. Silverman. The basic problem is to\nestimate a mean vector given a vector of observations of the\nmean vector plus white noise, taking advantage of possible\nsparsity in the mean vector. Within a Bayesian formulation, the\nelements of the mean vector are modelled as having,\nindependently, a distribution that is a mixture of an atom of\nprobability at zero and a suitable heavy-tailed distribution.\nThe mixing parameter can be estimated by a marginal maximum\nlikelihood approach. This leads to an adaptive thresholding\napproach on the original data. Extensions of the basic method,\nin particular to wavelet thresholding, are also implemented\nwithin the package.",
  "NeedsCompilation": "no",
  "License": "GPL (>= 2)",
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    "description": "Research Assistant Prof, Human Genetics, U. Chicago; previously, Staff Scientist at Ancestry, postdoc & HFSP fellow at U. Chicago, & Ph.D. at UBC",
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    "postmed.laplace",
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    "wfromx",
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      "page": "beta.cauchy",
      "title": "Function beta for the quasi-Cauchy prior",
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        "beta.cauchy"
      ]
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      "page": "beta.laplace",
      "title": "Function beta for the Laplace prior",
      "topics": [
        "beta.laplace"
      ]
    },
    {
      "page": "ebayesthresh",
      "title": "Empirical Bayes thresholding on a sequence",
      "topics": [
        "ebayesthresh"
      ]
    },
    {
      "page": "ebayesthresh.wavelet",
      "title": "Empirical Bayes thresholding on the levels of a wavelet transform.",
      "topics": [
        "ebayesthresh.wavelet",
        "ebayesthresh.wavelet.dwt",
        "ebayesthresh.wavelet.splus",
        "ebayesthresh.wavelet.wd"
      ]
    },
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      "title": "Posterior mean estimator",
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        "postmean.cauchy",
        "postmean.laplace"
      ]
    },
    {
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      "title": "Posterior median estimator",
      "topics": [
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        "postmed",
        "postmed.cauchy",
        "postmed.laplace"
      ]
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      "title": "Find threshold from mixing weight",
      "topics": [
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        "laplace.threshzero",
        "tfromw"
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      "title": "Find thresholds from data",
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      "title": "Threshold data with hard or soft thresholding",
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      "title": "Find weight and inverse scale parameter from data if Laplace prior is used.",
      "topics": [
        "negloglik.laplace",
        "wandafromx"
      ]
    },
    {
      "page": "wfromt",
      "title": "Mixing weight from posterior median threshold",
      "topics": [
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      ]
    },
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      "title": "Find Empirical Bayes weight from data",
      "topics": [
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    },
    {
      "page": "wmonfromx",
      "title": "Find monotone Empirical Bayes weights from data.",
      "topics": [
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      ]
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      "title": "Estimation of a parameter in the prior weight sequence in the EbayesThresh paradigm.",
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