A sub-asymptotic model for bivariate threshold exceedances

2026-04-14

AI Summary

Existing extreme-value models struggle to flexibly characterize both marginal tail behavior and joint dependence structures of bivariate threshold exceedances under asymptotic independence. This work proposes a novel bivariate subasymptotic parametric model that, while ensuring convergence of the margins to the generalized Pareto distribution, naturally captures the evolution of extremal dependence with varying thresholds through its scale parameters. The model encompasses the standard multivariate generalized Pareto distribution as a limiting special case and accommodates a broad spectrum of tail dependence patterns. Inference is carried out via a likelihood-free neural Bayesian approach with tailored priors, enabling direct computation and interpretation of failure probabilities. Extensive simulations and an analysis of Belgian rainfall extremes demonstrate the model’s flexibility and the effectiveness of the proposed inference framework.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications, however, extremes are intrinsically multivariate, requiring models that capture both marginal tail behaviours and joint extremal dependencies. Under asymptotic dependence, the multivariate GP distribution represents a suitable modelling family, but when asymptotic independence arises, sub-asymptotic models are needed. In this work, we propose and study a flexible sub-asymptotic parametric class to model bivariate threshold exceedances. Our new model accommodates a broad range of tail dependence behaviours and contains the standardised multivariate GP distribution as a limiting case while retaining margins that converge to univariate GP tails. Our formulation allows extremal dependence to evolve naturally with the marginal parameters on the original data scale, facilitating direct computation and interpretation of failure probabilities. Model inference is done via a likelihood-free neural Bayes estimation approach, with tailored prior specifications. An extensive simulation study and an application to Belgian rainfall extremes illustrate the estimation framework and the flexibility of the model.

Problem

• extreme value theory
• asymptotic independence
• bivariate threshold exceedances
• tail dependence
• sub-asymptotic model

Innovation

• sub-asymptotic model
• bivariate threshold exceedances
• extremal dependence
• neural Bayes estimation
• generalized Pareto distribution