Laplace Correction of Confusion Matrices to Produce Statistically Representative Confidence Intervals
Bibliographic record
Abstract
During diagnostic algorithm development engine testing with implanted faults may be performed. The number of implanted faults is never large enough to truly capture the distribution in the confusion matrix. Misdiagnoses in particular are unlikely to be correctly represented. Misdiagnosis that could result in costly outcomes are frequently not captured in an implantation study, resulting in a deceptively reassuring zero value for the probability of it occurring. The Laplace correction can be applied to each element of the confusion matrix to improve the generated confidence interval. This also allows a confidence interval to be produced for zero value elements. Unfortunately, the choice of Laplace correction factor influences the size of the confidence interval, and without knowing the true distribution the best correction factor cannot be determined. The choice of correction factor depends on element probability, total sample size, number of faults and confidence level. The effect of the Laplace correction on the element probability is analytically examined to provide insight into the relative influence of the correction. This is followed by an examination of the influence of the element probability, total sample size, number of faults and confidence level on the required Laplace correction. This is achieved by sampling from known populations. A method of generating good confidence intervals on each element is proposed. This includes the production of a Laplace correction based on the sample size, number of faults and confidence level. This will allow consistent comparisons of Laplace corrected matrices rather than leaving the correction factor to each individual’s best engineering judgment.
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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 | 0.026 | 0.231 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".