Interpolation of Spatial Data

Some Theory for Kriging
1999
ISBN: 978-0-387-98629-6
Verlag: Springer

Buch, Englisch, 249 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1250 g

Reihe: Springer Series in Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Stein, Michael L.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Geowissenschaften Geologie Geodäsie, Kartographie, Fernerkundung
• Geowissenschaften Geographie | Raumplanung Geodäsie, Kartographie, GIS, Fernerkundung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Geowissenschaften Geologie GIS, Geoinformatik

Inhaltsverzeichnis

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.- 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.