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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)
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)
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)
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 heavy-tailed density γ , with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequences.(More)
Various aspects of the wavelet approach to nonparametric regression are considered , with the overall aim of extending the scope of wavelet techniques, to irregularly-spaced data, to regularly-spaced data sets of arbitrary size, to heteroscedastic and correlated data, and to data some of which may be downweighted or omitted as outliers. At the core of the(More)
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)
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)