title: A nonparametric empirical Bayes framework for large-scale multiple testing.
abstract: We propose a flexible and identifiable version of the 2-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the nonnull cases. We use a computationally efficient predictive recursion (PR) 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 nonnull density can give a much better fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607, USA. rgmartin@math.uic.edu
authors.forename: Ryan
authors.initials: R
authors.lastname: Martin
authors.forename: Surya T
authors.initials: ST
authors.lastname: Tokdar
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001943:Breast Neoplasms / Q000235:genetics; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D007938:Leukemia / Q000235:genetics; D016013:Likelihood Functions; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis