Bayesian linear models for cardinal paired comparison data
Bibliographic record
Abstract
This paper develops a methodology for Bayesian updating in normal linear models in situations where the parameter of interest is restricted to a linear subspace. The methodology is motivated by and applied to the calculation of posterior distributions for the merit parameters and ranks arising in paired comparison data. The Bayesian paradigm is found to be ideal for assessing and quantifying the uncertainty in ranking procedures. The methodology is illustrated using simulated data and applied to two data sets: a network meta–analysis example and to the ranking of teams in the National Basketball Association (NBA).
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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 | 0.113 | 0.243 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.009 | 0.004 |
| Research integrity | 0.004 | 0.009 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".