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Activity Number: 414 - Models for Environmental Processes
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract #301798 Presentation
Title: Penalized Basis Models for Very Large Spatial Data Sets
Author(s): Mitchell Krock* and William Kleiber and Stephen Becker
Companies: University of Colorado at Boulder and University of Colorado and University of Colorado
Keywords: graphical model; graphical lasso; sparsity

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. Computations follow from a majorization-minimization approach, a byproduct of which is a connection to the graphical lasso. The result is a flexible nonstationary spatial model that is adaptable to very large datasets. 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 substantially improves Akaike information criterion score.

Authors who are presenting talks have a * after their name.

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