Localisation of Geometric Anisotropy

Olhede, Sofia C.

doi:10.1109/tsp.2007.912894

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…1). The estimation of anisotropy parameters is a topic of ongoing interest in various engineering fields (Jiang, 2005;Okada et al, 2005;Feng et al, 2008;Olhede, 2008;Le Bihan et al, 2001;Xu and Choi, 2009;Richard and Bierme, 2010;Wang and Leckie, 2012) and in data assimilation (Weaver and Mirouze, 2013). In geostatistics, the anisotropy is typically modeled by estimating the empirical variogram in different directions and fitting anisotropic variogram models (Chilès and Delfiner, 2012).…”

Section: Introductionmentioning

confidence: 99%

Non-parametric approximations for anisotropy estimation in two-dimensional differentiable Gaussian random fields

Petrakis

Hristopulos

2016

Stoch Environ Res Risk Assess

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Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a reference axis and the aspect ratio of the principal correlation lengths. Since these parameters are unknown a priori, sample estimates are needed to define suitable spatial models for the interpolation of incomplete data. The distribution of the anisotropy statistics is determined by a non-Gaussian sampling joint probability density. By means of analytical calculations, we derive an explicit expression for the joint probability density function of the anisotropy statistics for Gaussian, stationary and differentiable random fields. Based on this expression, we obtain an approximate joint density which we use to formulate a statistical test for isotropy. The approximate joint density is independent of the autocovariance function and provides conservative probability and confidence regions for the * petrakis@mred.tuc.gr † Corresponding author; dionisi@mred.tuc.gr anisotropy parameters. We validate the theoretical analysis by means of simulations using synthetic data, and we illustrate the detection of anisotropy changes with a case study involving background radiation exposure data. The approximate joint density provides (i) a standalone approximate estimate of the anisotropy statistics distribution (ii) informed initial values for maximum likelihood estimation, and (iii) a useful prior for Bayesian anisotropy inference.

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