Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences

Details Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences

2005-10-05

arxiv.org/abs/physics/0510035v4

Physica A: Statistical Mechanics and its Applications, 365(1-2), 211-216 (2006)

Physics

Data Analysis, Statistics and Probability

10 pages, to appear in Physica A v4: Some typos corrected and grammatical changes

Scientific paper

10.1016/j.physa.2006.01.037

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.

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