Computing Exact Gaussian Likelihoods for Markov Random Field Models

• Activity Number: 17
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Joseph Guinness* and Ilse C.F. Ipsen
• Companies: North Carolina State University and North Carolina State University
• Keywords: CAR models ; spatial data ; sparsity ; GMRF

Abstract

We introduce new methods for efficiently computing the Gaussian likelihood for spatial models that consist of a Gaussian Markov random field with stationary covariances and an additive uncorrelated error term, when the data locations fall on a possibly incomplete regular grid. The calculations can be made exact up to machine precision and are efficient both in memory allocation and computation time and are particularly fast when the uncorrelated error term is not present. Our approach handles boundary effects and missing values in a natural fashion. Frequentist methods are highlighted, but the availability of the likelihood allows for Bayesian inference as well. We demonstrate our results in simulation and timing studies, as well as with an application to gridded satellite data, where we use the exact likelihood both for parameter estimation and model comparison.