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

TL;DR

This paper introduces the full-scale basis graphical lasso (FSBGL), a novel method for modeling large, nonstationary spatial datasets by combining low rank processes with sparse covariance models, optimized via a graphical lasso approach.

Contribution

The paper presents FSBGL, a new modeling framework that integrates low rank and sparse covariance structures with a graphical lasso, improving nonstationary spatial data analysis.

Findings

FSBGL outperforms existing models in capturing thermospheric temperature features.

The method effectively handles high-resolution, limited data scenarios.

It combines full-scale approximation with basis graphical lasso for better spatial modeling.

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.