Estimating the proportion of true null hypotheses using the pattern of observed<i>p</i>-values
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.
Bibliographic record
Abstract
Estimating the proportion of true null hypotheses, π0, has attracted much attention in the recent statistical literature. Besides its apparent relevance for a set of specific scientific hypotheses, an accurate estimate of this parameter is key for many multiple testing procedures. Most existing methods for estimating π0 in the literature are motivated from the independence assumption of test statistics, which is often not true in reality. Simulations indicate that most existing estimators in the presence of the dependence among test statistics can be poor, mainly due to the increase of variation in these estimators. In this paper, we propose several data-driven methods for estimating π0 by incorporating the distribution pattern of the observed p-values as a practical approach to address potential dependence among test statistics. Specifically, we use a linear fit to give a data-driven estimate for the proportion of true-null p-values in (λ, 1] over the whole range [0, 1] instead of using the expected proportion at 1−λ. We find that the proposed estimators may substantially decrease the variance of the estimated true null proportion and thus improve the overall performance.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.028 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it