Multivariate distributional modeling of low, moderate, and large intensities without threshold selection steps

2025-10-02

AI Summary

Modeling the full distribution of positive hydroclimatic variables (e.g., precipitation, streamflow) remains challenging: conventional threshold-based approaches suffer from subjectivity, disrupt distributional coherence, and scale poorly to multivariate settings. Method: We propose a threshold-free, unified multivariate extreme-value model built upon an extended generalized Pareto distribution (GPD). Leveraging radial–angular decomposition, we separately model intensity (radial component) and dependence structure (angular component). The radial distribution is estimated via a hybrid of maximum likelihood and Bernstein polynomial-based semiparametric estimation; angular parameters are flexibly modeled using multivariate regression. Contribution/Results: Our hierarchical inference framework demonstrates robust performance on both synthetic and real-world hydrological datasets. It consistently captures heavy-tailed marginal distributions and complex multivariate dependence structures, significantly enhancing objectivity, flexibility, and scalability compared to existing methods.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In fields such as hydrology and climatology, modelling the entire distribution of positive data is essential, as stakeholders require insights into the full range of values, from low to extreme. Traditional approaches often segment the distribution into separate regions, which introduces subjectivity and limits coherence. This is especially true when dealing with multivariate data. In line with multivariate extreme value theory, this paper presents a unified, threshold-free framework for modelling marginal behaviours and dependence structures based on an extended generalized Pareto distribution (EGPD). We propose decomposing multivariate data into radial and angular components. The radial component is modelled using a semi-parametric EGPD and the angular distribution is permitted to vary conditionally. This approach allows for sufficiently flexible dependence modelling. The hierarchical structure of the model facilitates the inference process. First, we combine classical maximum likelihood estimation (MLE) methods with semi-parametric approaches based on Bernstein polynomials to estimate the distribution of the radial component. Then, we use multivariate regression techniques to estimate the angular component's parameters. The model is evaluated through synthetic simulations and applied to hydrological datasets to exemplify its capacity to capture heavy-tailed marginals and complex multivariate dependencies without threshold specification.

Problem

• Modeling entire multivariate distributions without threshold selection
• Unified framework for marginal and dependence structures using EGPD
• Flexible modeling of radial and angular components in extremes

Innovation

• Unified threshold-free framework using extended generalized Pareto distribution
• Decomposing multivariate data into radial and angular components
• Combining maximum likelihood estimation with Bernstein polynomial approaches