Sensitivity Testing Using Expectiles with Applications in Extremes
Bibliographic record
Abstract
Climate change is leading to an increase in the severity and prevalence of natural catastrophes. From a statistical and actuarial perspective, it is desirable to measure the potential impact of changes in different aspects of these extreme events. Sensitivity analysis is used to measure and characterize uncertainty of a model based on these changes, where a baseline model includes a number of covariates mapped to an output via an aggregation function. Given a defined stress on the baseline distribution, a type of sensitivity analysis used in actuarial mathematics, Reverse Sensitivity Testing, is suitable for several types of models (including black box models) and uses different risk measures along with the Kullback–Leibler divergence (KL divergence) as a measure of discrepancy between the baseline probability measure and the stressed probability measure. An expansion of Reverse Sensitivity Testing is provided to include both a coherent and elicitable risk measure; expectiles. Since the KL divergence is considered to be a pessimistic divergence for extreme values, the Renyi divergence, which is a broader divergence, is included as an extension ideal for extreme events given a user specified order parameter. Both the KL divergence and the Renyi divergence are implemented on a standard normal random variable, a numerical example, and then applied to extreme loss data from a natural catastrophe that hit Western Canada in 2020.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.004 | 0.008 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".