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Created on 29th January 2016
We introduce a novel Empirical Bayes approach for large-scale hypothesis testing, including estimating False Discovery Rates (FDRs), and estimating effect sizes. Compared with existing approaches to FDR analysis, the method has two key differences. First, it assumes that the distribution of the actual (unobserved) effects being tested is unimodal, with a mode at 0. This "unimodal assumption" (UA), although natural in many contexts, is very different from assumptions usually made in FDR analyses, and yields more accurate inferences than existing methods provided that it holds. The UA also facilitates efficient and robust computation because estimating the unimodal distribution involves solving a simple convex optimization problem. Second, the method takes as its input two numbers for each test (an effect size estimate, and corresponding standard error), rather than the one number usually used (p value, or z score). When available, using two numbers instead of one helps account for variation in measurement precision across tests. It also facilitates the estimation of actual effect sizes, and our approach provides interval estimates (credible regions) for each effect in addition to measures of significance. To provide a bridge between interval estimates and significance measures we introduce the term "local false sign rate" to refer to the probability of getting the sign of an effect wrong, and argue that it is a superior measure of significance than the local FDR because it is both more generally applicable, and can be more robustly estimated. Our methods are implemented in an R package ashr available from http://github.com/stephens999/ashr.Show more
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