About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387986294

ISBN-139780387986296

eBay Product ID (ePID)610941

Product Key Features

Number of PagesXvii, 249 Pages

LanguageEnglish

Publication NameInterpolation of Spatial Data : Some Theory for Kriging

Publication Year1999

SubjectEarth Sciences / Geography, Probability & Statistics / General, Earth Sciences / Geology

TypeTextbook

Subject AreaMathematics, Science

AuthorMichael L. Stein

SeriesSpringer Series in Statistics Ser.

FormatHardcover

Dimensions

Item Height0.3 in

Item Weight44.1 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN98-044772

ReviewsFrom a review: GEODERMA "the book is written with great care and dedication. Soil geostatisticians that are not easily scared off by mathematics will find this book to be a rich source of inspiration for many years to come.", From a review: GEODERMA "the book is written with great care and dedication. Soil geostatisticians that are not easily scared off by mathematics will find this book to be a rich source of inspiration for many years to come." , From a review:GEODERMA"the book is written with great care and dedication. Soil geostatisticians that are not easily scared off by mathematics will find this book to be a rich source of inspiration for many years to come."

Number of Volumes1 vol.

IllustratedYes

Table Of Content1 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.

SynopsisA 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.

LC Classification NumberQA273.A1-274.9