Bayesian Analysis of Sparse Counts Obtained From the Unrelated Question Design
Why this work is in the frame
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Bibliographic record
Abstract
In sample surveys with sensitive items, sampled units may not respond or they respond untruthfully. Usually a negative answer is given when it is actually positive, thereby leading to an estimate of the population proportion of positives (sensitive proportion) that is too small. In our study, we have binary data obtained from the unrelated-question design, and both the sensitive proportion and the nonsensitive proportion are of interest. A respondent answers the sensitive item with a known probability, and to avoid non-identifiable parameters, at least two (not necessarily exactly two) different random mechanisms are used, but only one for each cluster of respondents. The key point here is that the counts are sparse (very small sample sizes), and we show how to overcome some of the problems associated with the unrelated question design. A standard approach to this problem is to use the expectation-maximization (EM) algorithm. However, because we consider only small sample sizes (sparse counts), the EM algorithm may not converge and asymptotic theory, which can permit normality assumptions for inference, is not appropriate; so we develop a Bayesian method. To compare the EM algorithm and the Bayesian method, we have presented an example with sparse data on college cheating and a simulation study to illustrate the properties of our procedure. Finally, we discuss two extensions to accommodate finite population sampling and optional responses.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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