Sparse matrix tools for Gaussian models on lattices

Abstract

Sparse matrix methods are considered for Gaussian models on lattices. The approach depends on the applicability of mixed model methodology, which is feasible when observational errors are present. Moreover, lattice models with nearest-neighbor interactions lead to a spatial variance-covariance matrix having a sparse inverse, and this lends itself to sparse-matrix manipulation. Modern technology involving the Cholesky decomposition and backward differentiation are described for prediction, parameter estimation, cross validation, and conditional simulation of spatial processes.