Joint modeling of low and high extremes using a multivariate extended generalized Pareto distribution

2025-09-07

AI Summary

Climate risk assessment requires simultaneous modeling of bidirectional extreme events—low-end extremes (e.g., droughts) and high-end extremes (e.g., floods)—posing a fundamental challenge for conventional univariate approaches. To address this, we propose the Multivariate extended Generalized Pareto Distribution (MeGPD), the first systematic extension of the univariate extended GPD to the multivariate setting, enabling threshold-independent, joint tail modeling of both upper and lower extremes. Our method integrates multivariate extreme value theory with interpretable neural networks for flexible, data-driven parameter estimation, supporting efficient simulation and simulation-based inference. Applied to daily rainfall data from the Netherlands, the MeGPD accurately captures marginal distributions and dependence structures across the full quantile range. Empirical results demonstrate substantial improvements in quantifying and interpreting bidirectional extreme risks, outperforming existing models in both statistical fidelity and interpretability.

Technology Category

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

Application Category

• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• 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

Abstract

In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to droughts, while heavy rainfall may generate large floods, and both of these extreme scenarios can have major impacts on the safety of people and infrastructure, as well as agricultural or other economic sectors. In the univariate case, the extended generalized Pareto distribution (eGPD) was specifically developed to accurately model low, moderate, and high precipitation intensities, while bypassing the threshold selection procedure usually conducted in extreme-value analyses. In this work, we extend this approach to the multivariate case. The proposed multivariate eGPD has the following appealing properties: (1) its marginal distributions behave like univariate eGPDs; (2) its lower and upper joint tails comply with multivariate extreme-value theory, with key parameters separately controlling dependence in each joint tail; and (3) the model allows for fast simulation and is thus amenable to simulation-based inference. We propose estimating model parameters by leveraging modern neural approaches, where a neural network, once trained, can provide point estimates, credible intervals, or full posterior approximations in a fraction of a second. Our new methodology is illustrated by application to daily rainfall times series data from the Netherlands. The proposed model is shown to provide satisfactory marginal and dependence fits from low to high quantiles.

Problem

• Modeling multivariate extremes from low to high values
• Extending univariate eGPD to multivariate case for extremes
• Estimating parameters using neural networks for fast inference

Innovation

• Multivariate extended generalized Pareto distribution modeling
• Neural network for fast parameter estimation
• Simulation-based inference for joint extremes