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arXiv · 2505.01318

Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso

Matthew LeDuc·William Kleiber·Tomoko Matsuo
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Abstract

We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical Gaussian Markov random field model. The utilization of a low rank and compactly-supported covariance structure combines the full-scale approximation and the basis graphical lasso; we term this new approach the full-scale basis graphical lasso (FSBGL). Estimation employs a graphical lasso-penalized likelihood, which is optimized using a difference-of-convex scheme. We illustrate the proposed approach on synthetic fields as well as with a challenging high-resolution simulation dataset of the thermosphere. In a comparison against state-of-the-art spatial models, the FSBGL performs better at capturing salient features of the thermospheric temperature fields, even with limited available training data.

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Matthew LeDuc, William Kleiber, Tomoko Matsuo. 2025-05-02. Modeling Large Nonstationary Spatial Data with the Full-Scale Basis Graphical Lasso. https://doi.org/10.1016/j.spasta.2026.101007

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