Determination of exact sample sizes in the Bayesian estimation of the difference of two proportions
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Bibliographic record
Abstract
Summary. Using generalized hypergeometric functions in several variables in a Bayesian context, we compute the exact minimum double-sample size (n1, n2) required in the Bernoulli sampling of two independent populations, so that the expected length (or the maximum length) of the highest posterior density credible interval of P=P1 − P2 is less than a preset quantity, where P1 and P2 are two independent proportions. This precise and computer-intensive approach permits the treatment of this Bayesian sample size determination problem under very general hypotheses and also provides a relationship between the minimal values of n1 and n2. Similar results are derived in an applied Bayesian decision theory context, with a quadratic loss function, and the criteria used are now the posterior risk, the Bayes risk and the expected value of sample information.
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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 | 0.002 | 0.019 |
| 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 | 0.001 |
| 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