Estimating deformations of isotropic Gaussian random fields on the plane

Abstract

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on ${\mathbb{R}}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package--from model assumptions to algorithmic recovery of the deformation--for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.

Published in at http://dx.doi.org/10.1214/009053607000000893 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)