Abstract
The microarray gene expression applications have greatly stimulated the statistical research on the massive multiple hypothesis tests problem. There is now a large body of literature in this area and basically five paradigms of massive multiple tests: control of the false discovery rate (FDR), estimation of FDR, significance threshold criteria, control of family-wise error rate (FWER) or generalized FWER (gFWER), and empirical Bayes approaches. This paper contains a technical survey of the developments of the FDR-related paradigms, emphasizing precise formulation of the problem, concepts of error measurements, and considerations in applications. The goal is not to do an exhaustive literature survey, but rather to review the current state of the field.