Non-parametric Estimation of Geometric Anisotropy from Environmental Sensor Network Measurements

This paper addresses the estimation of geometric anisotropy parameters from scattered data in two dimensional spaces. The parameters involve the orientation angle of the principal anisotropy axes and the anisotropy ratio (i.e., the ratio of the principal correlation lengths). The mathematical background is based on the covariance Hessian identity (CHI) method developed in [3, 1]. CHI links the expectation of the first-order sample derivatives tensor with the Hessian matrix of the covariance function [6]. The paper focuses on the application of CHI to samples that require segmentation into clusters, either due to sampling density variations or due to systematic changes in the process values. A non-parametric isotropy test is also presented. Finally, a composite (real and synthetic) data set is used to investigate the impact of CHI anisotropy estimation on spatial interpolation with ordinary kriging

Systematic Detection of Anisotropy in Spatial Data Obtained from Environmental Monitoring Networks

The efficient mapping of environmental hazards requires the development of methods for the analysis of the spatial distributions sampled from environmental monitoring networks. We focus on the detection of the geometric (elliptic) anisotropy parameters of spatially distributed variables represented by means of random fields. The geostatistical estimation of anisotropy parameters often relies on empirical methods or maximum likelihood approaches that are impractical for large data sets. We present a non-parametric, computationally fast method for the identification of the anisotropy parameters of scalar random fields. The method uses sample based estimates of the spatial derivatives that are related through closed form expressions to the anisotropy parameters. We investigate the performance of the method on synthetic samples on regular and irregular supports. We estimate the anisotropy of radioactivity distributions (gamma dose rates) obtained from the EURDEP (EUropean Radiological Data Exchange Platform)

On approximation for fractional stochastic partial differential equations on the sphere

This paper gives the exact solution in terms of the Karhunen-Lo\`{e}ve expansion to a fractional stochastic partial differential equation on the unit sphere $\mathbb{S}^{2}\subset \mathbb{R}^{3}$ with fractional Brownian motion as driving noise and with random initial condition given by a fractional stochastic Cauchy problem. A numerical approximation to the solution is given by truncating the Karhunen-Lo\`{e}ve expansion. We show the convergence rates of the truncation errors in degree and the mean square approximation errors in time. Numerical examples using an isotropic Gaussian random field as initial condition and simulations of evolution of cosmic microwave background (CMB) are given to illustrate the theoretical results.Comment: 28 pages, 7 figure