JSM 2004 - Toronto

Abstract #300300

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Activity Number: 208
Type: Invited
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: ENAR
Abstract - #300300
Title: Intrinsic Autoregressions and the de Wijs Process
Author(s): Debashis Mondal*+ and Julian Besag
Companies: University of Washington, Seattle and University of Washington
Address: Department of Statistics, , ,
Keywords: intrinsic autoregressions ; de Wijs process ; approximation
Abstract:

Intrinsic auto regressions are Markov random fields that have a rigorous interpretation as generalizations of random walks to higher dimensions. They have been used as prior distributions to represent spatial variation at different scales, from microscopy to agriculture to epidemiology to astronomy. Homogeneous Gaussian intrinsic auto regressions on rectangular arrays are nonstationary limiting versions of stationary conditional auto regressions. The most used first-order scheme induces well-defined distributions for all contrasts. We evaluate the associated variogram and show that this provides a close approximation to the variogram of the corresponding conformally invariant integrated de Wijs process in the plane, provided the cells of the array are not too elongated. This suggests that the more easily used auto regressions display an approximate invariance to changes of scale, which has also been our experience in agricultural applications.

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