CLIMB talk with Aaditya Ramdas

Since the publication of the seminal Benjamini-Hochberg paper (the most cited paper in statistics), it has been an open problem how the "closure principle" applies to controlling the false discovery rate (FDR). As background, the closure principle was formulated in a seminal 1976 Biometrika paper, and states that every procedure for controlling the familywise error rate (FWER) can be recovered or improved via "closed testing".

We fully settle this open problem by finally developing a closure principle not only for FDR, but every error metric that is an expectation (including the classical one for FWER as a special case). Also surprisingly, our developments crucially hinge on the modern concept of e-values, which perhaps explains why it had not been discovered in the past 30 years despite explicit efforts.

This theoretical advance has immediate implications for practice: it leads to surprising improvements to both modern and classical FDR methods (eg: Benjamini-Yekutieli's famous 2001 procedure is strictly improved, as is the e-Benjamini-Hochberg procedure), and it also allows for practitioners to choose the error metric post-hoc (and sometimes the error level itself).

https://arxiv.org/abs/2509.02517 is the preprint, joint work with Ziyu Xu, Aldo Solari, Lasse Fischer, Rianne de Heide, Jelle Goeman (it is actually a merge of two simultaneous papers). https://www.nowpublishers.com/article/Details/STA-002 is a new book on e-values, also available as a PDF on my webpage.