Bibliographic record
Abstract
Summary This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of $p$-values without making any assumptions about their dependence structure. A result by Rüschendorf (1982) and, independently, Meng (1993) implies that the $p$-values can be combined by scaling up their arithmetic mean by a factor of 2, and no smaller factor is sufficient in general. A similar result by Mattner about the geometric mean replaces 2 by e. Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we extend these results to generalized means; in particular, we show that $K$ $p$-values can be combined by scaling up their harmonic mean by a factor of $\log K$ asymptotically as $K$ tends to infinity. This leads to a generalized version of the Bonferroni–Holm procedure. We also explore methods using weighted averages of $p$-values. Finally, we discuss the efficiency of various methods of combining $p$-values and how to choose a suitable method in light of data and prior information.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.044 | 0.143 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".