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Interpolation of Spatial Data Some Theory for Kriging

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...

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Bibliographic Details
Main Author: Stein, Michael L.
Format: eBook
Language:English
Published: New York, NY Springer New York 1999, 1999
Edition:1st ed. 1999
Series:Springer Series in Statistics
Subjects:
Geology
Statistical Theory And Methods
Geography
Statistics 
Probability Theory
Statistics In Engineering, Physics, Computer Science, Chemistry And Earth Sciences
Earth Sciences
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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 Jeffreys’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 Matérn model
  • 6.6 A numerical study of the Fisherinformation matrix under the Matérn model
  • 6.7 Maximum likelihood estimation for a periodic version of the Matérn model

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