Computational Instability of Inverse of Spatial Covariance Matrices

Abstract

Computing an inverse of a covariance matrix is a common computational component in statistics. For example, Gaussian likelihood function includes the inverse of a covariance matrix. Spatial prediction called Kriging requires computation of the inverse of a spatial covariance matrix as well. For the computation of the inverse of a spatial covariance matrix, numerically unstable results can be found when the observation locations are getting denser. In this paper, we investigate when computational instability in calculating the inverse of a spatial covariance matrix makes maximum likelihood estimator or Kriging unreasonable for a Mat'ern covariance model. Also, some possible approaches to relax such computational instability are discussed. Keywords: MLE, Kriging, Mat'ern covariance models, ill-conditioned.