Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences
Data Analysis, Statistics and Probability
2012-04-12 v4 Statistics Theory
Statistics Theory
Abstract
The spatial structure of fluctuations in spatially inhomogeneous processes can be modeled in terms of Gibbs random fields. A local low energy estimator (LLEE) is proposed for the interpolation (prediction) of such processes at points where observations are not available. The LLEE approximates the spatial dependence of the data and the unknown values at the estimation points by low-lying excitations of a suitable energy functional. It is shown that the LLEE is a linear, unbiased, non-exact estimator. In addition, an expression for the uncertainty (standard deviation) of the estimate is derived.
Cite
@article{arxiv.physics/0510035,
title = {Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences},
author = {D. T. Hristopulos},
journal= {arXiv preprint arXiv:physics/0510035},
year = {2012}
}
Comments
10 pages, to appear in Physica A v4: Some typos corrected and grammatical changes