Estimating geometric anisotropy in spatial point patterns

Authors

Affiliations

Tuomas Rajala

Chalmers University of Technology and the University of Gothenburg

Aila Särkkä

Chalmers University of Technology and the University of Gothenburg

Claudia Redenbach

University of Kaiserslautern

Martina Sormani

University of Kaiserslautern

Abstract

Anisotropy in stationary spatial point patterns is investigated. We develop a two-stage non-parametric method for quantifying geometric anisotropy arising for example when the pattern is compressed or stretched. First, we fit ellipsoids to the pattern of pairwise difference vectors to estimate the direction of anisotropy. Then, we estimate the scale of anisotropy by identifying the back-transformation resulting in the most isotropic pattern. We demonstrate the applicability of the method mainly for regular patterns by numerical examples, and use it to improve the estimation of compression in 3D polar ice air bubble patterns.

Figure 6 (EDML only): Estimated linear transformations in the polar ice core datasets. The perspective plot is of a sphere transformed by the grand average of each dataset, and the front-side-top plots depict the intersection of planes, whose normals are the main axes, with different ellipsoids: The grand average (thick line, light color), circle for reference (thick, black) and ellipsoid estimates in the sub-samples (thin, light).