English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Spatially referenced data often have autocovariance functions with ellipticalisolevel contours, a property known as geometric anisotropy. The anisotropyparameters include the tilt of the ellipse (orientation angle) with respect toa reference axis and the aspect ratio of the principal correlation lengths.Since these parameters are unknown a priori, sample estimates are needed todefine suitable spatial models for the interpolation of incomplete data. Thedistribution of the anisotropy statistics is determined by a non-Gaussiansampling joint probability density. By means of analytical calculations, wederive an explicit expression for the joint probability density function of theanisotropy statistics for Gaussian, stationary and differentiable randomfields. Based on this expression, we obtain an approximate joint density whichwe use to formulate a statistical test for isotropy. The approximate jointdensity is independent of the autocovariance function and provides conservativeprobability and confidence regions for the anisotropy parameters. We validatethe theoretical analysis by means of simulations using synthetic data, and weillustrate the detection of anisotropy changes with a case study involvingbackground radiation exposure data. The approximate joint density provides (i)a stand-alone approximate estimate of the anisotropy statistics distribution(ii) informed initial values for maximum likelihood estimation, and (iii) auseful prior for Bayesian anisotropy inference.

Non-Parametric Approximations for Anisotropy Estimation in Two-dimensional Differentiable Gaussian Random Fields