Modelling probability summation for the detection of multiple stimuli under the assumptions of signal detection theory
Bibliographic record
Abstract
In general there are two ways in which multiple stimuli can sum to threshold: by probability summation or by additive summation (of which linear summation is a special case). Probability summation (PS) is still often modelled using the long-refuted High Threshold Theory (HTT), in spite of the fact that most researchers believe that Signal Detection Theory (SDT) is the better model. Studies which do model PS under SDT often use Monte Carlo simulations to perform the calculations, but this method is prohibitively slow when many thousands of calculations are required, as when fitting psychometric functions with PS models and estimating bootstrap errors on the fitted parameters and model goodnesses-of-fit. We provide numerical integration formulae for calculating, on the assumptions of SDT, the proportion correct detections for n independently detected stimuli, each subject to a non-linear transducer τ, while Q channels are being monitored, and for an M-AFC task. We show how the equations can be used to simulate psychometric functions in order to determine how parameters such as the Weibull threshold and slope vary with n, τ and Q. We also show how the equations can be used to fit actual psychometric functions from a binocular summation experiment in order to obtain estimates of τ and to determine whether probability or additive summation is the better model of the data. Meeting abstract presented at VSS 2015
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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 | 0.006 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".