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AuthorStein, Michael L. author
TitleInterpolation of Spatial Data [electronic resource] : Some Theory for Kriging / by Michael L. Stein
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1494-6
Descript XVII, 249 p. online resource

SUMMARY

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


CONTENT

1 Linear Prediction -- 1.1 Introduction -- 1.2 Best linear prediction -- 1.3 Hilbert spaces and prediction -- 1.4 An example of a poor BLP -- 1.5 Best linear unbiased prediction -- 1.6 Some recurring themes -- 1.7 Summary of practical suggestions -- 2 Properties of Random Fields -- 2.1 Preliminaries -- 2.2 The turning bands method -- 2.3 Elementary properties of autocovariance functions -- 2.4 Mean square continuity and differentiability -- 2.5 Spectral methods -- 2.6 Two corresponding Hilbert spaces -- 2.7 Examples of spectral densities on 112 -- 2.8 Abelian and Tauberian theorems -- 2.9 Random fields with nonintegrable spectral densities -- 2.10 Isotropic autocovariance functions -- 2.11 Tensor product autocovariances -- 3 Asymptotic Properties of Linear Predictors -- 3.1 Introduction -- 3.2 Finite sample results -- 3.3 The role of asymptotics -- 3.4 Behavior of prediction errors in the frequency domain -- 3.5 Prediction with the wrong spectral density -- 3.6 Theoretical comparison of extrapolation and ointerpolation -- 3.7 Measurement errors -- 3.8 Observations on an infinite lattice -- 4 Equivalence of Gaussian Measures and Prediction -- 4.1 Introduction -- 4.2 Equivalence and orthogonality of Gaussian measures -- 4.3 Applications of equivalence of Gaussian measures to linear prediction -- 4.4 Jeffreysโ{128}{153}s law -- 5 Integration of Random Fields -- 5.1 Introduction -- 5.2 Asymptotic properties of simple average -- 5.3 Observations on an infinite lattice -- 5.4 Improving on the sample mean -- 5.5 Numerical results -- 6 Predicting With Estimated Parameters -- 6.1 Introduction -- 6.2 Microergodicity and equivalence and orthogonality of Gaussian measures -- 6.3 Is statistical inference for differentiable processes possible? -- 6.4 Likelihood Methods -- 6.5 Matรฉrn model -- 6.6 A numerical study of the Fisher information matrix under the Matรฉrn model -- 6.7 Maximum likelihood estimation for a periodic version of the Matรฉrn model -- 6.8 Predicting with estimated parameters -- 6.9 An instructive example of plug-in prediction -- 6.10 Bayesian approach -- A Multivariate Normal Distributions -- B Symbols -- References


Mathematics Earth sciences Geology Geography Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics for Engineering Physics Computer Science Chemistry and Earth Sciences Geology Geography general Earth Sciences general



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