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Wavelet threshold estimators for data with stationary correlated noise are constructed by the following prescription. First, form the discrete wavelet transform of the data points. Next, apply a level-dependent soft threshold to the individual coeecients, allowing the thresholds to depend on the level in the wavelet transform. Finally, transform back to… (More)

This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If… (More)

In standard wavelet methods, the empirical wavelet coefficients are thresholded term by term, on the basis of their individual magnitudes. Information on other coefficients has no influence on the treatment of particular coefficients. We propose and investigate a wavelet shrinkage method that incorporates information on neighboring coefficients into the… (More)

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density γ, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If… (More)

Bacterial communities provide important services. They break down pollutants, municipal waste and ingested food, and they are the primary means by which organic matter is recycled to plants and other autotrophs. However, the processes that determine the rate at which these services are supplied are only starting to be identified. Biodiversity influences the… (More)

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavytailed density γ , with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences. If… (More)

- Chris C. A Spencer, Panos Deloukas, +6 authors Gil McVean
- PLoS genetics
- 2006

In humans, the rate of recombination, as measured on the megabase scale, is positively associated with the level of genetic variation, as measured at the genic scale. Despite considerable debate, it is not clear whether these factors are causally linked or, if they are, whether this is driven by the repeated action of adaptive evolution or molecular… (More)

Suppose that a sequence of unknown parameters is observed subject to independent Gaussian noise. The EbayesThresh package in the S language implements a class of Empirical Bayes thresholding methods that can take advantage of possible sparsity in the sequence, to improve the quality of estimation. The prior for each parameter in the sequence is a mixture of… (More)

- B. W. Silverman
- 2015

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. SUMMARY A technique… (More)