In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization when and why point estimates accurately recover behavior. this paper, develop flexible practical confidence intervals that asymptotic frequentist coverage estimands...

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach and a full Bayes (FB) approach. We then apply EB and FB to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian...

This article concerns the canonical empirical Bayes problem of estimating normal means under squared-error loss. General empirical estimators are derived which are asymptotically minimax and optimal. Uniform convergence and the speed of convergence are considered. The general empirical Bayes estimators are compared with the shrinkage estimators of Stein (1956) and James and Stein (1961). Estima...

For the problem of variable selection for the normal linear model, selection criteria such as , C p ,  and  have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that...

Epidemiological studies often involve multiple comparisons, and may therefore report many "false positive" statistically significant findings simply because of the large number of statistical tests involved. Traditional methods ofadjustment for multiple comparisons, such as the Bonferroni method, may induce investigators to ignore potentially important findings, because they do not take account...