A nonparametric empirical Bayes framework for large-scale multiple testing

Abstract

We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally efficient predictive recursion marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonparametric empirical Bayes testing procedure, which we call PRtest, based on thresholding the estimated local false discovery rates. Simulations and real-data examples demonstrate that, compared to existing approaches, PRtest's careful handling of the non-null density can give a much better fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.

18 pages, 4 figures, 3 tables

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• The Statistical Analysis of fMRI Data
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• Convergence rate for predictive recursion estimation of finite mixtures
• An approximate Bayesian marginal likelihood approach for estimating finite mixtures
• Variational approximations of empirical Bayes posteriors in high-dimensional linear models
• On nonparametric estimation of a mixing density via the predictive recursion algorithm
• Permutation-based uncertainty quantification about a mixing distribution
• Revisiting consistency of a recursive estimator of mixing distributions
• Model Selection for Maternal Hypertensive Disorders with Symmetric Hierarchical Dirichlet Processes
• Estimating a mixing distribution on the sphere using predictive recursion
• Anytime valid and asymptotically optimal inference driven by predictive recursion
• A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions
• A deconvolution path for mixtures