Benjamini–Hochberg FDR control under correlated Gaussian tests
Follow the latest progress by email.
Does ordinary Benjamini–Hochberg testing control false discovery rate at its nominal level for correlated two-sided Gaussian p-values? Independence and positive regression dependence provide known positive settings; arbitrary Gaussian correlation is the question.
Why it matters and what counts as progress
Why it matters: A dependent Gaussian example would delimit false-discovery control beyond independence and positive regression dependence.
What counts as progress: Prove control under broader dependence assumptions or give a specified Gaussian model with rigorously excessive false discovery rate.
How the problem developed
- 1995 · Theorem [1]
Yoav Benjamini and Yosef Hochberg Introduced the step-up procedure and proved false discovery rate control under independent test statistics.
- 2001 · Partial result [2]
Yoav Benjamini and Daniel Yekutieli Showed BH control under positive regression dependence and gave a harmonic-factor modification valid under arbitrary dependence.
- 13 Jul 2026 · Reported claim [3]
Edgar Dobriban, with GPT-5.6 Pro Reported a correlated two-sided Gaussian factor model where BH exceeds nominal FDR 0.01, with a rigorous interval-arithmetic lower bound above 0.0104.
AI contribution
The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
In a specified three-block Gaussian factor model with 96N true nulls and 4N nonnulls, ordinary Benjamini–Hochberg testing at level 0.01 has false discovery rate greater than 0.0104 for all sufficiently large N when applied to correlated two-sided Gaussian p-values.
Sources
- Benjamini and Hochberg, Controlling the false discovery rate
- Benjamini and Yekutieli, The control of the false discovery rate in multiple testing under dependency
- Dobriban, The Benjamini–Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
- Benjamini–Hochberg FDR under correlated Gaussian tests
Website timeline
Publication dates and editorial changes.
AI-found Gaussian counterexample to Benjamini–Hochberg FDR control