Remy MacDonald | Searcharxiv

arXiv2025

A Dimension-Reduced Multivariate Spatial Model for Extreme Events: Balancing Flexibility and Scalability

Modeling extreme precipitation and temperature is vital for understanding the impacts of climate change, as hazards like intense rainfall and record-breaking temperatures can result in severe consequences, including floods, droughts, and wildfires. Gaining insight into the spatial variation and interactions between these extremes is critical for effective risk management, early warning systems, and informed policy-making. However, challenges such as the rarity of extreme events, spatial dependencies, and complex cross-variable interactions hinder accurate modeling. We introduce a novel framework for modeling spatial extremes, building upon spatial generalized extreme value (GEV) models. Our approach incorporates a dimension-reduced latent spatial process to improve scalability and flexibility, particularly in capturing asymmetry in cross-covariance structures. This Joint Latent Spatial GEV model (JLS-GEV) overcomes key limitations of existing methods by providing a more flexible framework for inter-variable dependencies. In addition to addressing event rarity, spatial dependence and cross-variable interactions, JLS-GEV supports nonstationary spatial behaviors and independently collected data sources, while maintaining practical fitting times through dimension reduction. We validate JLS-GEV through extensive simulation studies, demonstrating its superior performance in capturing spatial extremes compared to baseline modeling approaches. Application to real-world data on extreme precipitation and temperature in the southeastern United States highlights its practical utility. While primarily motivated by environmental challenges, this framework is broadly applicable to interdisciplinary studies of spatial extremes in interdependent natural processes.

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arXiv2022

Flexible Basis Representations for Modeling Large Non-Gaussian Spatial Data

Nonstationary and non-Gaussian spatial data are common in various fields, including ecology (e.g., counts of animal species), epidemiology (e.g., disease incidence counts in susceptible regions), and environmental science (e.g., remotely-sensed satellite imagery). Due to modern data collection methods, the size of these datasets have grown considerably. Spatial generalized linear mixed models (SGLMMs) are a flexible class of models used to model nonstationary and non-Gaussian datasets. Despite their utility, SGLMMs can be computationally prohibitive for even moderately large datasets (e.g., 5,000 to 100,000 observed locations). To circumvent this issue, past studies have embedded nested radial basis functions into the SGLMM. However, two crucial specifications (knot placement and bandwidth parameters), which directly affect model performance, are typically fixed prior to model-fitting. We propose a novel approach to model large nonstationary and non-Gaussian spatial datasets using adaptive radial basis functions. Our approach: (1) partitions the spatial domain into subregions; (2) employs reversible-jump Markov chain Monte Carlo (RJMCMC) to infer the number and location of the knots within each partition; and (3) models the latent spatial surface using partition-varying and adaptive basis functions. Through an extensive simulation study, we show that our approach provides more accurate predictions than competing methods while preserving computational efficiency. We demonstrate our approach on two environmental datasets - incidences of plant species and counts of bird species in the United States.

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