Positive Regression Dependency and the False Discovery Rate

The Benjamini-Hochberg method is a mainstay of FDR control in fMRI analysis. However, despite its widespread usage, BH is only known to be valid under a condition known as Positive Regression Dependency on each Subset (PRDS) (c.f. Benjamini & Yekutieli (2001)). This condition, which aims to capture the intuitive idea of "positive dependency between variables" is often understated in the literature, but is crucial to the method's proof. In this talk, I will aim to (1) survey the literature on Positive Regression Dependency, explaining where the notion originated and, hopefully, reducing confusion surrounding its statement and (2) work through a sketch proof of Benjamini & Yekutieli (2001) to highlight why PRDS is necessary for the method's validity.

This talk was originally given in the NeuroImaging Statistics Oxford (NISOx) reading group on the 19th February 2024.