2011/06/30 by Ryan Martin, Surya T. Tokdar · 41 citations
Decision Sciences · Mathematics · #Artificial intelligence #Bayes factor #Bayes' theorem #Bayesian probability #Computer science #Data mining #Econometrics #Mathematics #Mixture model #Nonparametric statistics #Null (SQL) #Null distribution #Null hypothesis #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Statistical hypothesis testing #Statistics #Test statistic #stat.CO #stat.ME
paper · pdf · doi:10.1093/biostatistics/kxr039
published in Biostatistics 13(3), 427-439 (Oxford University Press) · 18 pages, 4 figures, 3 tables
arxiv created 2011/10/01 · openalex publication_date 2011/11/14 · arxiv updated 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.