Modelling and Inference for Extremal Events
Bibliographic record
Abstract
Extreme events are frequently observed in nature and in human activities; they tend to have severe and often negative impact. For this reason they are wellstudied, and the underlying body of work is usually referred to as extreme value theory. The theory often deals with the behavior in the tail of probability distributions or data sets. A key notation is that of heavy-tailed probability distributions. Univariate heavy-tailed distributions exhibit interesting mathematical properties practical for modelling purposes. However, many types of univariate heavy-tailed distributions do not have natural multivariate extensions. Another area of interest in extreme value theory is that of the clustering of extremes in stationary sequences. Inference of cluster sizes tends to be difficult, partly due to the scarcity of data. Clustering also introduces heavy serial dependence in extremal observations, which in turn influences statistical analysis. This thesis seeks to address the aforementioned problems and difficulties. Key contributions include: a multivariate model for a particular class of heavy-tailed distributions, the subexponential distributions, that allows for the approximation of ruin probabilities; a multilevel approach to extremal inference that partially addresses the issue of data scarcity and that improves the variance of extremal estimators; and an algorithmic method to reduce of serial dependence in extremal inference
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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 | 0.011 | 0.063 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".