Implementing Gaussian Spatial Autoregressive Models for Massive Georeferenced Data Sets: An Example from Peru

• Activity Number: 666
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Daniel A. Griffith*+
• Companies: U. of Texas at Dallas
• Keywords: eigenvalue ; Jacobian term ; massive georeferenced dataset ; maximum likelihood estimate (MLE) ; remotely sensed image ; spatial autoregression

Abstract

The literature proposes approximations to the determinant of a positive definite n-by-n spatial covariance matrix (the Jacobian term) for Gaussian spatial autoregressive models that fail to support the analysis of massive georeferenced datasets. This paper surveys this literature, recalls and refines much simpler Jacobian approximations, presents selected eigenvalue estimation techniques, summarizes validation results (for estimated eigenvalues, Jacobian approximations, and parameter estimation), and illustrates the estimation of the autocorrelation parameter in a spatial autoregressive model. Data are from a 4850-by-4988 Landsat image containing La Oroya, Peru, where a spectral signature appears from fumes produced over the years by a mining refinery, and for which n = 24,191,800. The principal contribution of this paper is to the implementation of spatial autoregressive model specifications for any size of georeferenced dataset. Its specific additions to the literature include: (1) new, more efficient estimation algorithms; (2) an approximation of the Jacobian term for remotely sensed data forming incomplete rectangular regions; (3) issues of inference; and, (4) timing results.