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.
Interpolation of Spatial Data
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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."
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30 of 31 people found the following review helpful:
5.0 out of 5 stars
great theoretical treatment of spatial data analysis and kriging,
By
This review is from: Interpolation of Spatial Data: Some Theory for Kriging (Springer Series in Statistics) (Hardcover)
Michael Stein got his Ph.D. in Statistics from Stanford University under the direction of Paul Switzer. I also studied at Stanford years earlier and also learned about kriging from Switzer. Kriging is a very popular technique for interpolation of spatial data between measurement points. It is an optimal linear technique when the spatial covariance structure is known. It has many practical applications to pollution data, geological data etc. Stein develops the theory as far as he can for the case when the covariance structure is unknown and must be estimated based on the measurement data.
The theoretical development requires some advanced mathematical knowledge on the part of the reader including advanced probability, Fourier analysis and Hilbert spaces. The second order properties of random fields and results on Gaussian measures needed for the development of key results are covered in Chapter 2. Those interested in the practical aspects of kriging can omit the proofs and just concentrate on the results. Chapter 6 provides important practical information. Although difficult to digest, a careful reading of the book will provide insight into what is good and what is bad about the way kriging is commonly implemented. The bootstrap approach to assessing the accuracy of kriging predictions is briefly discussed in section 6.8 page 202. This text concentrates on Stein's development of fixed domain asymptotics. It does not provide a broad overview of kriging. That can be found in Noel Cressie's book. It also does not deal with other aspects of interpolation such as nonlinear interpolation, estimation for non-Gaussian processes or the connections with splines. Nevertheless this is a landmark text that should be on the shelf of any statistician interested in spatial data.
4.0 out of 5 stars
worth reading,
By MRM "M" (Mexico) - See all my reviews
This review is from: Interpolation of Spatial Data: Some Theory for Kriging (Springer Series in Statistics) (Hardcover)
It is not an easy book, but the book has very interesting ideas about kriging. In particular, it studies deeply the situation where the number of data points increases on a fixed interval.
1 of 3 people found the following review helpful:
4.0 out of 5 stars
A good book,
By A Customer
This review is from: Interpolation of Spatial Data: Some Theory for Kriging (Springer Series in Statistics) (Hardcover)
Several chapters are not easy to read because of the material, also is not comprehensive about kriging; but despite that,it has a lot of interesting results and it is worth of reading.
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Inside This Book
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First Sentence:
This book investigates prediction of a spatially varying quantity based on observations of that quantity at some set of locations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
centered systematic sample, real linear manifold, differentiable random fields, evenly spaced observations, square differentiable, empirical semivariogram, underlying random field, irregular term, actual mse, isotropic random field, autocovariance function, mean square derivatives, differentiable processes, mean square continuous, asymptotic mse, geostatistical literature, turning bands method, neighboring observations, high frequency behavior, eyeball estimate, linear unbiased prediction, profile log likelihood, stationary random fields, nearest observation, domain asymptotics Key Phrases - Capitalized Phrases (CAPs): (learn more)
Plausible Approximation, Prove Theorem, Bochner's Theorem, Plots of Matérn, Eoeó Eoei New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This book investigates prediction of a spatially varying quantity based on observations of that quantity at some set of locations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
centered systematic sample, real linear manifold, differentiable random fields, evenly spaced observations, square differentiable, empirical semivariogram, underlying random field, irregular term, actual mse, isotropic random field, autocovariance function, mean square derivatives, differentiable processes, mean square continuous, asymptotic mse, geostatistical literature, turning bands method, neighboring observations, high frequency behavior, eyeball estimate, linear unbiased prediction, profile log likelihood, stationary random fields, nearest observation, domain asymptotics Key Phrases - Capitalized Phrases (CAPs): (learn more)
Plausible Approximation, Prove Theorem, Bochner's Theorem, Plots of Matérn, Eoeó Eoei New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
61
books
cite this book:
See all 61 books citing this book
- Nonparametric and Semiparametric Models by Wolfgang Karl Härdle in Back Matter
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- Modern Multidimensional Scaling: Theory and Applications (Springer Series in Statistics) by I. Borg in Back Matter
- Resampling Methods for Dependent Data (Springer Series in Statistics) by S. N. Lahiri in Back Matter
- Introduction to Rare Event Simulation by James Bucklew in Back Matter
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