Bibliographic record
Abstract
AbstractIn this note, we give an explicit expression for the quantile of a mixture of tworandom variables. We carefully examine all possible cases of discrete and continuousvariables with possibly unbounded support. The result is useful for finding boundson the Value-at-Risk of risky portfolios when only partial information is available(Bernard and Vanduffel (2014)). ∗ Carole Bernard, Department of Statistics and Actuarial Science at the University of Waterloo (email:c3bernar@uwaterloo.ca). † Corresponding author : Steven Vanduffel, Department of Economics and Political Sciences at VrijeUniversiteit Brussel (VUB). (e-mail: steven.vanduffel@vub.ac.be). ‡ C. Bernard gratefully acknowledges support from the Natural Sciences and Engineering ResearchCouncil of Canada, the Humboldt Research Foundation and the hospitality of the chair of mathematicalstatistics of Technische Universit¨at Mu¨nchen where the paper was completed. S. Vanduffel acknowledgesthe financial support of the BNP Paribas Fortis Chair in Banking.
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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 | 0.007 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.015 | 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".