Nonstationary Modeling With Sparsity for Spatial Data via the Basis Graphical Lasso. Issue 2 (3rd June 2021)

• Record Type: Journal Article
• Authors: Krock, Mitchell; Kleiber, William; Becker, Stephen
• Is Part Of: Journal of computational and graphical statistics. Volume 30:Issue 2(2021)
• Page Start: 375
• Page End: 389
• Publication Date: 2021-06-03
• Subjects: Graphical lasso -- Graphical model -- Spatial basis functions; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2020.1811103
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential equations, and empirical orthogonal functions all fall within this basic framework. Given a particular basis, stochastic dependence relies on flexible modeling of the coefficients. Under a Gaussianity assumption, we propose a graphical model family for the stochastic coefficients by parameterizing the precision matrix. Sparsity in the precision matrix is encouraged using a penalized likelihood framework—we term this approach the basis graphical lasso. Computations follow from a majorization-minimization (MM) approach, a byproduct of which is a connection to the standard graphical lasso. The result is a flexible nonstationary spatial model that is adaptable to very large datasets with multiple realizations. We apply the model to two large and heterogeneous spatial datasets in statistical climatology and recover physically sensible graphical structures. Moreover, the model performs competitively against the popular LatticeKrig model in predictive cross-validation but improves the Akaike information criterion score and a log score for the quality of the joint predictive distribution.