Comparison of Accuracy Properties of Point Estimators for the Ratio of Binomial Proportions with the Inverse-Direct Sampling Scheme
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Bibliographic record
Abstract
We continue our investigation into the estimation of the ratio of Binomial proportions. We concentrate on point estimation and its accuracy properties. A problem of the point estimation for a ratio of two proportions using data from two independent Bernoulli samples is considered. In this article we mostly discuss the case when the first sample is obtained using the Inverse sampling scheme and the second one using the Direct Binomial sampling scheme. Our goal is to show that the normal approximations, which are relatively simple, for estimates of the ratio are reliable for the construction of point estimators with reliable accuracy properties. The main criterion of our judgment is the bias and mean squared error. The main accuracy characteristics of estimators corresponding to all possible combinations of sampling schemes are investigated by the Monte-Carlo method. Mean values and mean squared errors of point estimators are collected in tables, and some recommendations for the application of each estimators are presented.
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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 | 0.012 |
| 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