Spatial Process Estimates - IMAGe

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Kriging as a smoother Suppose the errors are uncorrelated Normals with variance σ 2 . ρK = COV (g, y) = COV (g, g) and COV (y) = (ρK + σ 2 I) ĝ = ρK(ρK + σ 2 I) −1 y = K(K + λI) −1 y = A(λ)y 8
My geostatistics/BLUE overhead For any covariance and any smoothing matrix (not just A above) we can easily derive the prediction variance. Question: Find the minimum of over all choices of A. E [ (g(x) − ĝ(x)) 2] The answer: The Kriging weights ... or what we would do if we used the Gaussian process and the conditional distribution. Folklore and intuition: The spatial estimates are not very sensitive if one uses suboptimal weights, especially if the observations contain some measurement error. It does matter for measures of uncertainty. 9
Page 1 and 2: Spatial Process Estimates SAMSI Sum
Page 3 and 4: The additive model Given n pairs of
Page 5 and 6: A review of the conditional normal
Page 7: The Kriging weights Conditional dis
Page 11 and 12: BLUE/Universal Kriging Find d by Ge
Page 13 and 14: The spline connection Basis functio
Page 15 and 16: Identifying a covariance function T
Page 17 and 18: Correlations among ozone In many ca
Page 19 and 20: 50 Sensitivity to the covariance Ex
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Spatial Process Estimates - IMAGe

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