Benjamini-Hochberg FDR Under Correlated Gaussian Tests
Does the Benjamini-Hochberg procedure always control the false-discovery rate at its nominal level for correlated two-sided Gaussian p-values? A factor model gives at nominal level .
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Statistics
- Posed by
- —
- Year posed
- 2006
- Years open
- 20y
- Solved
- 2026-07-13
- Model
- GPT-5.6 Pro
- Vendor
- OpenAI
- Collaborators
- Edgar Dobriban
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The counterexample was obtained by GPT-5.6 Pro and carefully checked by the author, with a rigorous interval-arithmetic certificate valid for all sufficiently large numbers of hypotheses.
Verification
Author-checked arXiv preprint with an interval-arithmetic certificate. Not yet peer-reviewed.
Source
arXiv:2607.12208 - The Benjamini-Hochberg procedure can fail to control the FDR