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In modern high-throughput data analysis, researchers perform a large numberof statistical tests, expecting to find perhaps a small fraction of significanteffects against a predominantly null background. Higher Criticism (HC) wasintroduced to determine whether there are any nonzero effects; more recently,it was applied to feature selection, where it provides a method for selectinguseful predictive features from a large body of potentially useful features,among which only a rare few will prove truly useful. In this article, we reviewthe basics of HC in both the testing and feature selection settings. HC is aflexible idea, which adapts easily to new situations; we point out simpleadaptions to clique detection and bivariate outlier detection. HC, althoughstill early in its development, is seeing increasing interest frompractitioners; we illustrate this with worked examples. HC is computationallyeffective, which gives it a nice leverage in the increasingly more relevant"Big Data" settings we see today. We also review the underlying theoretical"ideology" behind HC. The Rare/Weak (RW) model is a theoretical frameworksimultaneously controlling the size and prevalence of useful/significant itemsamong the useless/null bulk. The RW model shows that HC has importantadvantages over better known procedures such as False Discovery Rate (FDR)control and Family-wise Error control (FwER), in particular, certain optimalityproperties. We discuss the rare/weak phase diagram, a way to visualize clearlythe class of RW settings where the true signals are so rare or so weak thatdetection and feature selection are simply impossible, and a way to understandthe known optimality properties of HC.

Higher Criticism for Large-Scale Inference, Especially for Rare and Weak Effects