Bayesian inference on sparse multinomial data using smoothed Dirichlet distribution with an application to COVID-19 data
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.069 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".