How to combine direction cues optimally
Bibliographic record
Abstract
Many perceptual tasks require estimating a direction in space. Often several directional cues are available, such visual and gravitational cues to the subjective vertical, or visual and auditory cues to the direction of an object. In work on the subjective vertical, researchers have developed a heuristic vector summation model that has no deep theoretical motivation, but that accounts well for the direction and reliability of observers’ direction estimates when multiple cues are available, and that can accommodate directional cues ranging over all possible directions (Mittelstaedt, 1983). In work on combining visual and auditory cues to direction, researchers have used statistically motivated cue combination models that were originally developed for linear quantities such as depth, not circular or spherical quantities such as direction, and hence work only over a limited range of cue directions (Alais and Burr, 2004). Here we present a new model of directional cue combination that combines the advantages of both previous approaches. We develop a statistical theory of cue combination based on the von Mises distribution, the analog on the circle of the normal distribution on the line. We show that this theory differs in important ways from the theory of linear cue combination, e.g., a combined direction estimate can be less certain than any of the individual cues that were used to calculate it. We also show that the vector summation model developed empirically by previous investigators is an excellent approximation to our theory, meaning that it is a nearly optimal way of combining directional cues.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".