Closed-Form Solution of the Unit Normal Loss Integral in Two-Dimensions
Bibliographic record
Abstract
In Value of Information (VoI) analysis, the unit normal loss integral (UNLI) frequently emerges as a solution for the computation of various VoI metrics. However, one limitation of the UNLI has been that its closed-form solution is available for only one dimension, and thus can be used for comparisons involving only two strategies (where it is applied to the scalar incremental net benefit). We derived a closed-form solution for the two-dimensional UNLI, enabling closed-form VoI calculations for three strategies. We verified the accuracy of this method via simulation studies. A case study based on a three-arm clinical trial was used as an example. VoI methods based on the closed-form solutions for the UNLI can now be extended to three-decision comparisons, taking a fraction of a second to compute and not being subject to Monte Carlo error. An R implementation of this method is provided as part of the predtools package (https://github.com/resplab/predtools/).
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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 | 0.012 | 0.056 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.016 | 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".