Resampling-Based Empirical Bayes multiple Testing Procedures for Controlling Generalized Tail Probability Error Rates

Multiple testing problems currently encountered in biomedical and genomic research are characterized by a large number of hypotheses (in the thousands, or even millions), concerning high-dimensional multivariate distributions, with complex and unknown dependence structures among variables. For instance, for the identification of differentially expressed or co-expressed genes as in Chapter 9, microarray datasets typically consist of thousands of expression measures for fewer than one hundred observational units. As argued in Section 3.4.1, multiple testing procedures (MTP) controlling the proportion of false positives among the rejected hypotheses are particularly appealing for large-scale testing problems. However, only a handful of approaches are currently available for controlling such Type I error rates.