Post-selection inference for e-value based confidence intervals
Bibliographic record
Abstract
Suppose that one can construct a valid (1 -)-confidence interval (CI) for each of parameters of potential interest.If a data analyst uses an arbitrary data-dependent criterion to select some subset of parameters, then the aforementioned CIs for the selected parameters are no longer valid due to selection bias.We design a new method to adjust the intervals in order to control the false coverage rate (FCR).The main established method is the "BY procedure" by Benjamini and Yekutieli (JASA, 2005).The BY guarantees require certain restrictions on the selection criterion and on the dependence between the CIs.We propose a new simple method which, in contrast, is valid under any dependence structure between the original CIs, and any (unknown) selection criterion, but which only applies to a special, yet broad, class of CIs that we call e-CIs.To elaborate, our procedure simply reports (1 -||/)-CIs for the selected parameters, and we prove that it controls the FCR at for confidence intervals that implicitly invert e-values; examples include those constructed via supermartingale methods, via universal inference, or via Chernoff-style bounds, among others.The e-BY procedure is admissible, and recovers the BY procedure as a special case via a particular calibrator.Our work also has implications for post-selection inference in sequential settings, since it applies at stopping times, to continuously-monitored confidence sequences, and under bandit sampling.We demonstrate the efficacy of our procedure using numerical simulations and real A/B testing data from Twitter.
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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 | 0.060 | 0.348 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.003 | 0.008 |
| 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".