Aggregating statistical evidence under exchangeability: Schrab et al. beat Bonferroni's conservatism
_onionesque · x · 2026-10-30
Antonin Schrab, Rajen Shah, Arthur Gretton and Ilmun Kim posted "Aggregation of Statistical Evidence under Exchangeability" (arXiv:2607.15823, 97 pages).
The paper aggregates statistical evidence under unknown, complex dependence using group-invariance/permutation constructions: evidence is aggregated across statistics within each transformed dataset, then calibrated across transformations. Key results:
- Single-batch aggregation uniformly improves critical values over deterministic calibrations valid under arbitrary dependence (including Bonferroni), while adapting to the unknown dependence structure;
- Finite-sample power and adaptivity theory is developed;
- Extensions include a sequential alpha-spending version allowing early rejection, and a two-batch scheme separating standardization from calibration to support learned aggregation rules and cut computation;
- Applications to adaptive nonparametric testing and conformal prediction sharpen existing methods.
onionesque notes the approach combines dependent tests via shared permutations without Bonferroni's excessive conservatism, with finite-sample error control ensured by exchangeability.
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