Interpolation of Spatial Data Some Theory for Kriging [Hardcover]

A summary of past work and a description of new approaches to thinking about kriging, commonly used in the prediction of a random field based on observations at some set of locations in mining, hydrology, atmospheric sciences, and geography.Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging.1 Linear Prediction.- 1.1 Introduction.- 1.2 Best linear prediction.- Exercises.- 1.3 Hilbert spaces and prediction.- Exercises.- 1.4 An example of a poor BLP.- Exercises.- 1.5 Best linear unbiased prediction.- Exercises.- 1.6 Some recurring themes.- The Mat?rn model.- BLPs and BLUPs.- Inference for differentiable random fields.- Nested models are not tenable.- 1.7 Summary of practical suggestions.- 2 Properties of Random Fields.- 2.1 Preliminaries.- Stationarity.- Isotropy.- Exercise.- 2.2 The turning bands method.- Exercise.- 2.3 Elementary properties of autocovariance functions.- Exercise.- 2.4 Mean square continuity and differentiability.- Exercises.- 2.5 Spectral methods.- Spectral representation of a random field.- Bochners Theorem.- Exercises.- 2.6 Two corresponding Hilbert spaces.- An application to mean square differentiability.- Exercises.- 2.7 Examples of spectral densities on 112.- Rational spectral densities.- Principal irregular term.- Gaussian model.- Triangular autocovariance functions.- Mat?rn class.- Exercises.- 2.8 Abelian and Tauberian theorems.- Exercises.- 2.9 Random fields with nonintegrable spectral densities.- Intrinsic random functions.- Semivariograms.- Generalized random fields.- Exercises.- 2.10 Isotropic autocovariance functions.- ló`