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)

Cited by in corpus (8)

• Nonstationary covariance models for global data
• Composite Gaussian process models for emulating expensive functions
• Amplitude and phase variation of point processes
• Regression-based covariance functions for nonstationary spatial modeling
• Consistent estimates of deformed isotropic Gaussian random fields on the plane
• Estimating the smoothness of a Gaussian random field from irregularly spaced data via higher-order quadratic variations
• Interpolation of nonstationary high frequency spatial-temporal temperature data
• Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment