Computational Instability of Inverse of Spatial Covariance Matrices

• Activity Number: 58
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Chae Young Lim* and Wei-Ying Wu and Chien-Hung Chen
• Companies: Seoul National University and National Dong Hwa University and National Dong Hwa University
• Keywords: MLE ; Kriging ; Matern covariance model ; Ill-conditioned

Abstract

Computing an inverse of a covariance matrix is very common computational component in statistics. For example, Gaussian likelihood function involves the inverse of a covariance matrix. Spatial prediction called Kriging involves the 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 work, we investigate why and when computational instability in calculating the inverse of a spatial covariance matrix makes maximum likelihood estimator (MLE) or Kriging unreasonable for the Matérn covariance model. Also, some possible approaches to relax such computational instability are discussed.