FDR control

False discovery rate control in multiple testing. We have hypothesis $H_1,\dots ,H_K$. The true nulls are $N\subset [K]$. If $D\subset [K]$ are indices of discoveries (i.e., rejections) by some testing procedure, the number of false discoveries is $F_D=|D\cap N|$. The false discovery rate is $F_D/|D|$, which we want to be low. Since it’s a random variable, we want to control $\mathbb{E}[F_D/|D|]$.

This criteria was introduced by Benjamini and Hochberg in the most widely cited paper in statistics. They introduced a procedure for achieving FDR control in the same paper: the BH procedure. The e-BH procedure is a similar procedure but using e-values instead of p-values, and can handle arbitrary dependence.