Methods to Approximate a Spatial Likelihood

• Activity Number: 208
• Type: Invited
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Montserrat Fuentes*+
• Companies: North Carolina State University
• Keywords: Whittle's likelihood ; spectral domain ; satellite data ; irregular lattices ; covariance ; Fourier transform

Abstract

Likelihood approaches for large, irregularly spaced spatial datasets are often very difficult, if not infeasible, to use due to computational limitations. Even when we can assume normality, exact calculations of the likelihood for a Gaussian spatial process observed at n locations requires O(n^3) operations. We present a version of Whittle's approximation to the Gaussian log likelihood for spatial lattices with missing values. This method requires O(n^2log_2 n) operations and does not involve calculating determinants. If the usual biased sample covariance is used in this approximated likelihood method, the estimated covariance parameters are efficient only in one dimension due to the edge effect. To remove this edge effect, we introduce a new data taper, a circular taper, that gives more tapering to the corner observations. We present simulations and theoretical results to show the benefits and the performance of proposed methods. We apply this likelihood method to sea surface temperature satellite data in the presence of clouds.