Semiparametric Copula‐Based Confidence Intervals on Level Curves for the Evaluation of the Risk Level Associated to Bivariate Events
Bibliographic record
Abstract
ABSTRACT If is a random pair with distribution function , one can define the level curve of probability as the values of such that . This level curve is at the base of bivariate versions of return periods for the assessment of risk associated with extreme events. In most uses of bivariate return periods, the values taken by on this level curve are accorded equal significance. This paper adopts an innovative point‐of‐view by showing how to build confidence sets for the values of a pair of continuous random variables on a level curve. To this end, it is shown that the conditional distribution of given that the pair belongs to the level curve can be written in terms of the copula that characterizes its dependence structure. This allows for the definition of confidence sets on the level curve. It is suggested that the latter be estimated semi‐parametrically, where the copula is assumed to belong to a given parametric family, and the marginals are replaced by their empirical counterparts. Formulas are derived for the Farlie–Gumbel–Morgenstern, Archimedean, Normal, and Student copulas. The methodology is illustrated on the risk level associated with the daily concentration of atmospheric pollutants.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".