Bayesian inference on sparse multinomial data using smoothed Dirichlet distribution with an application to COVID-19 data
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Bibliographic record
Abstract
We develop a Bayesian approach for estimating multinomial cell probabilities using a smoothed Dirichlet prior. The most important feature of the smoothed Dirichlet prior is that it forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet prior. We propose a shrinkage-type estimator using this Bayesian approach to estimate multinomial cell probabilities. The proposed estimator allows us to borrow information across other multinomial populations and cell categories simultaneously to improve the estimation of cell probabilities, especially in a context of sparsity with ordered categories. We demonstrate the proposed approach using COVID-19 data and estimate the distribution of positive COVID-19 cases across age groups for Canadian health regions. Our approach allows improved estimation in smaller health regions where few cases have been observed.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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