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Record W4405425641 · doi:10.48550/arxiv.2408.11307

Improved thresholds for e-values

2024· preprint· en· W4405425641 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenuearXiv (Cornell University) · 2024
Typepreprint
Languageen
FieldDecision Sciences
TopicAdvanced Statistical Process Monitoring
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsStatisticsMathematicsPsychology

Abstract

fetched live from OpenAlex

The rejection threshold used for e-values and e-processes is by default set to $1/α$ for a guaranteed type-I error control at $α$, based on Markov's and Ville's inequalities. This threshold can be wasteful in practical applications. We discuss how this threshold can be improved under additional distributional assumptions on the e-values; some of these assumptions are naturally plausible and empirically observable, without knowing explicitly the form or model of the e-values. For small values of $α$, the threshold can roughly be improved (divided) by a factor of $2$ for decreasing or unimodal densities, and by a factor of $e$ for decreasing or unimodal-symmetric densities of log-transformed e-values. Moreover, we propose to use the supremum of comonotonic e-values, which is shown to preserve the type-I error guarantee. We also propose some preliminary methods to boost e-values in the e-BH procedure under some distributional assumptions while controlling the false discovery rate. Through a series of simulation studies, we demonstrate the effectiveness of our proposed methods in various testing scenarios, showing enhanced power.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.911
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0020.003
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.267
GPT teacher head0.334
Teacher spread0.067 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it