Wee Extremes: EVA 2023 Data Challenge
This project showcases my work as part of the “Wee Extremes” team during the EVA (2023) Conference Data Challenge. It is summarized in the peer-reviewed article, “A wee exploration of techniques for risk assessments of extreme events” (Extremes, 2024).
Motivation & Objectives
Estimating risk measures for extreme events—such as high quantiles or joint exceedance probabilities—in environmental data is challenging due to:
- Non‑stationarity (covariate effects)
- Sparse data in the tail
- Multivariate dependence structure
- Extrapolation to unobserved extreme levels
The EVA challenge provided a structured testbed (four tasks: C1–C4) involving both univariate and multivariate extremes in a simulated “Utopia” environment. The data were designed to mimic real environmental settings while preserving controlled truth for evaluation.
Our goal was to build a composite methodology combining multiple statistical tools to robustly estimate extreme quantiles, tail probabilities, and joint behavior under uncertainty.
Methodological Approach
Key components of our approach include:
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Non-Stationary Modeling
Extended traditional Extreme Value Analysis (EVA) by incorporating covariate effects, primarily through GAM based Generalized Pareto Distribution (GPD) parameterizations to model the conditional tail. -
Tail Extrapolation
Rigorously compared different methods (e.g., GAM-GPD vs. Quantile Extrapolation) in Task C1 to select the optimal approach for predicting unobserved extreme levels. -
Dependence Structure
Used Copula frameworks for multivariate tasks (C3, C4) to effectively model joint exceedance probabilities beyond the limitations of marginal modeling. -
Uncertainty Quantification
We used Block Bootstrap methods to assess and validate model uncertainty. Crucially, the Block Bootstrap allowed us to perform model selection validation by generating pseudodata that preserves dependence structure, enabling us to test model performance against unobserved extreme data (far-tail extrapolation). -
Stability & Robustness
Employed Model Averaging across bootstrap samples and Dimensionality Reduction techniques to mitigate overfitting and stabilize extreme quantile estimates.
Key Findings & Insights 💡
Our results highlighted the critical impact of tail assumptions on risk estimates:
-
Validation is Key for Extrapolation
Our use of the Block Bootstrap was essential for validating model choices, especially when extrapolating to extreme return levels beyond the observed data range. -
Tail Behavior is Critical
Methods assuming lighter tail behavior than reality tended to severely underestimate risk, particularly for extreme return levels. -
Dependence is Decisive
Errors in tail dependence modeling can severely bias joint exceedance probability estimates (Tasks C3, C4). -
Stability Matters
Model averaging and bootstrap techniques were crucial to stabilize extreme quantile estimates and provide reliable uncertainty bounds.
Outcome & Publication
-
The work produced a peer-reviewed article:
“A wee exploration of techniques for risk assessments of extreme events” (Extremes, 2024). -
We contributed methodology that blends EVA, copula theory, dimensionality reduction, and bootstrap averaging.