Bibliographic record
Abstract
Bayesian cue combination models have been used to examine how human observers combine information from several cues to form estimates of linear quantities like depth. Here we develop an analogous theory for circular quantities like planar direction. The circular theory is broadly similar to the linear theory but differs in significant ways. First, in the circular theory the combined estimate is a nonlinear function of the individual cue estimates. Second, in the circular theory the mean of the combined estimate is affected not only by the means of individual cues and the weights assigned to individual cues but also by the variability of individual cues. Third, in the circular theory the combined estimate can be less certain than the individual estimates, if the individual estimates disagree with one another. Fourth, the circular theory does not have some of the closed-form expressions available in the linear theory, so data analysis requires numerical methods. We describe a vector sum model that gives a heuristic approximation to the circular theory's behavior. We also show how the theory can be extended to deal with spherical quantities like direction in three-dimensional space.
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".