Breakthrough Tracker record
Correlated two-sided Gaussian tests can defeat the Benjamini–Hochberg guarantee
An explicit correlated Gaussian factor model, backed by an interval-arithmetic certificate, has asymptotic false discovery rate above 0.0104 when Benjamini–Hochberg is run at nominal level 0.01. A follow-on paper extends the negative result.
← Back to the filtered Breakthrough Tracker
- Stable ID
math-benjamini-hochberg-correlated-gaussian-2026- Revision
math-benjamini-hochberg-correlated-gaussian-2026.v2- Field
- Mathematics · Mathematical statistics
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Current · Expert-supported preprint with reproducible certificate
- Last checked
AI role
The paper states that GPT-5.6 Pro produced the proof and that Dobriban carefully checked it.
Record details
- Problem or result
- False-discovery-rate control for Benjamini–Hochberg under unrestricted Gaussian correlation
- Authors
- Edgar Dobriban
- Institutions
- University of Pennsylvania
- Result date
- Preprint submitted July 13, 2026
Why it matters
The primary counterexamples delimit a standard multiple-testing guarantee under unrestricted Gaussian dependence, while an independent v4 analysis now gives a sharper two-sided upper bound with a matching leading constant for a class of correlations.
Limits
The result does not invalidate Benjamini–Hochberg under independence or its established positive-dependence conditions. Both the primary and follow-on analyses remain unrefereed preprints, and the matching leading constant is proved only for specified correlation classes rather than every dependence structure.
Sources
- Primary: Edgar Dobriban, The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
- Independent: Independent v4 analysis with sharper two-sided bound
- Independent: Independent technical explainer with scope caveats
Correction and revision history
- Added on 2026-07-22 with the dependence assumptions and small numerical excess made explicit to prevent overstatement.
- 2026-10-19 — Updated the independent follow-on to v4, which sharpens the two-sided upper bound and matches the leading constant for a class of correlations; retained expert-supported, unrefereed status.
Machine-readable: JSON v1 · CSV v1 · Schema v1
This individual record remains noindex until a story-specific featured image passes Kingy’s rendered-pixel visual review. The source-linked tracker hub remains the public index.