Modeling high and low extremes with a novel dynamic spatio-temporal model

2025-08-02

AI Summary

Existing dynamic spatiotemporal models often rely on Gaussian assumptions, limiting their capacity to characterize extremes; conversely, conventional spatial extreme-value models typically neglect temporal dependence and focus solely on upper-tail joint behavior. To address these limitations, we propose a novel dynamic spatiotemporal extreme-value model that—uniquely—integrates both heavy- and light-tailed distributions via a flexible, spatially and temporally varying tail index. This enables unified modeling of both upper and lower extremes (e.g., extreme pollution and extreme cleanliness) along with their full spatiotemporal dependence structure. Grounded in extreme-value theory and Bayesian inference, the model supports principled uncertainty quantification and robust imputation of missing data. Evaluated on hourly PM₂.₅ measurements across the U.S. Midwest, it demonstrates superior predictive accuracy and robustness over state-of-the-art alternatives, accurately identifying and forecasting both high- and low-end extremes.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the underlying mechanisms and enhance informed decision-making, a flexible model capable of accommodating extremes is necessary. Existing dynamic spatio-temporal statistical models exhibit limitations in capturing extremes when assuming Gaussian error distributions, whereas the current models for spatial extremes mostly assume temporal independence and are focused on joint upper tails at two or more locations. Here, we introduce a new class of dynamic spatio-temporal models that capture both high and low extremes using a mixture of heavy- and light-tailed distributions with varying tail indices. Our framework flexibly identifies extremal dependence and independence in both space and time with uncertainty quantification and supports missing data prediction, as in other dynamic spatio-temporal models. We demonstrate its effectiveness using a large reanalysis dataset of hourly particulate matter in the Central United States.

Problem

• Modeling high and low extremes in spatio-temporal data
• Overcoming Gaussian limitations in capturing extreme events
• Quantifying extremal dependence in space and time

Innovation

• Dynamic spatio-temporal model with mixed tail distributions
• Flexible extremal dependence identification in space-time
• Missing data prediction with uncertainty quantification