Premium
Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison
Author(s) -
Bickel David R.
Publication year - 2014
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12064
Subject(s) - statistics , confidence interval , mathematics , bayes' theorem , confidence distribution , estimator , inference , coverage probability , false discovery rate , null hypothesis , interval estimation , statistical hypothesis testing , econometrics , bayesian probability , computer science , artificial intelligence , biochemistry , chemistry , gene
Summary Empirical Bayes methods of estimating the local false discovery rate (LFDR) by maximum likelihood estimation (MLE), originally developed for large numbers of comparisons, are applied to a single comparison. Specifically, when assuming a lower bound on the mixing proportion of true null hypotheses, the LFDR MLE can yield reliable hypothesis tests and confidence intervals given as few as one comparison. Simulations indicate that constrained LFDR MLEs perform markedly better than conventional methods, both in testing and in confidence intervals, for high values of the mixing proportion, but not for low values. (A decision‐theoretic interpretation of the confidence distribution made those comparisons possible.) In conclusion, the constrained LFDR estimators and the resulting effect‐size interval estimates are not only effective multiple comparison procedures but also they might replace p ‐values and confidence intervals more generally. The new methodology is illustrated with the analysis of proteomics data.