Many statistical problems involve data from thousands of parallel cases. Eachcase has some associated effect size, and most cases will have no effect. It isoften important to estimate the effect size and the local or tail-area falsediscovery rate for each case. Most current methods do this separately, and mostare designed for normal data. This paper uses an empirical Bayes mixture modelapproach to estimate both quantities together for exponential family data. Theproposed method yields simple, interpretable models that can still be usednonparametrically. It can also estimate an empirical null and incorporate itfully into the model. The method outperforms existing effect size and falsediscovery rate estimation procedures in normal data simulations; it nearlyacheives the Bayes error for effect size estimation. The method is implementedin an R package (mixfdr), freely available from CRAN.
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