Spatial Statistics and Spatio-Temporal Data
Covariance Functions and Directional Properties
Published on 6. January 2011
240 pages
978-0-470-97492-6 (ISBN)
Description
In the spatial or spatio-temporal context, specifying the correctcovariance function is fundamental to obtain efficient predictions,and to understand the underlying physical process of interest. Thisbook focuses on covariance and variogram functions, their role inprediction, and appropriate choice of these functions inapplications. Both recent and more established methods areillustrated to assess many common assumptions on these functions,such as, isotropy, separability, symmetry, and intrinsiccorrelation.
After an extensive introduction to spatial methodology, the bookdetails the effects of common covariance assumptions and addressesmethods to assess the appropriateness of such assumptions forvarious data structures.
Key features:
* An extensive introduction to spatial methodology including asurvey of spatial covariance functions and their use in spatialprediction (kriging) is given.
* Explores methodology for assessing the appropriateness ofassumptions on covariance functions in the spatial,spatio-temporal, multivariate spatial, and point patternsettings.
* Provides illustrations of all methods based on data andsimulation experiments to demonstrate all methodology and guide toproper usage of all methods.
* Presents a brief survey of spatial and spatio-temporal models,highlighting the Gaussian case and the binary data setting, alongwith the different methodologies for estimation and model fittingfor these two data structures.
* Discusses models that allow for anisotropic and nonseparablebehaviour in covariance functions in the spatial, spatio-temporaland multivariate settings.
* Gives an introduction to point pattern models, includingtesting for randomness, and fitting regular and clustered pointpatterns. The importance and assessment of isotropy of pointpatterns is detailed.
Statisticians, researchers, and data analysts working withspatial and space-time data will benefit from this book as well aswill graduate students with a background in basic statisticsfollowing courses in engineering, quantitative ecology oratmospheric science.
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Michael Sherman
Spatial Statistics and Spatio-Temporal Data - Covariance Functions and Directional Properties
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12/2010
Wiley
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Spatial Statistics and Spatio-Temporal Data
Covariance Functions and Directional Properties
Book
11/2010
Wiley
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Person
Michael Sherman, Professor of Statistics, Texas A&MUniversity
Michael Sherman has done extensive research on re-samplingmethods for temporally or spatially dependent data and spatialstatistics. He has published various papers in JASA, Biometrics andJRSS-B. In 2000 he created a course in Spatial Statistics atTexas A&M University and has given over 35 invitedpresentations at University seminars, ASA meetings and specialtopic meetings.
Content
Preface.
1 Introduction.
1.1 Stationarity.
1.2 The Effect of Correlation in Estimation and Prediction.
1.3 Texas Tidal Data.
2 Geostatistics.
2.1 A Model for Optimal Prediction and Error Assessment.
2.2 Optimal Prediction (Kriging).
2.3 Prediction Intervals.
2.4 Universal Kriging.
2.5 The Intuition Behind Kriging.
3 Variogram and Covariance Models and Estimation.
3.1 Empirical Estimation of the Variogram or CovarianceFunction.
3.2 On the Necessity of Parametric Variogram and CovarianceModels.
3.3 Covariance and Variogram Models.
3.4 Convolution Methods and Extensions.
3.5 Parameter Estimation for Variogram and CovarianceModels.
3.6 Prediction for the Phosphorus Data.
3.7 Nonstationary Covariance Models.
4 Spatial Models and Statistical Inference.
4.1 Estimation in the Gaussian Case.
4.2 Estimation for Binary Spatial Observations.
5 Isotropy.
5.1 Geometric anisotropy.
5.2 Other Types of Anisotropy.
5.3 Covariance Modelling under Anisotropy.
5.4 Detection of Anisotropy: The Rose Plot.
5.5 Parametric Methods to Assess Isotropy.
5.6 Nonparametric Methods of Assessing Anisotropy.
5.7 Assessment of Isotropy for General Sampling Designs.
5.8 An Assessment of Isotropy for the Longleaf Pine Sizes.
6 Space-time Data.
6.1 Space-Time Observations.
6.2 Spatio-Temporal Stationarity and Spatio-TemporalPrediction.
6.3 Empirical Estimation of the Variogram, Covariance Models,and Estimation.
6.4 Spatio-Temporal Covariance Models.
6.5 Space-Time Models.
6.6 Parametric Methods of Assessing Full Symmetry and Space-TimeSeparability.
6.7 Nonparametric Methods of Assessing Full Symmetry andSpace-Time Separability.
6.8 Nonstationary Space Time Covariance Models.
7 Spatial Point Patterns.
7.1 The Poisson Process and Spatial Randomness.
7.2 Inhibition Models.
7.3 Clustered Models.
8 Isotropy for Spatial Point Patterns.
8.1 Some Large Sample Results.
8.2 A Test for Isotropy.
8.3 Practical Issues.
8.4 Numerical Results.
8.5 An Application to Leukemia Data.
9 Multivariate Spatial and Spatio-temporal Models.
9.1 CoKriging.
9.2 An Alternative to CoKriging.
9.3 Multivariate Covariance Functions.
9.4 Testing and Assessing Intrinsic Correlation.
9.5 Numerical Experiments.
9.6 A Data Application to Pollutants.
9.7 Discussion.
10 Resampling for Correlated Observations.
10.1 Independent Observations.
10.2 Other Data Structures.
10.3 Model Based Bootstrap.
10.4 Model Free Resampling Methods.
10.5 Spatial Resampling.
10.6 Model Free Spatial Resampling.
10.7 Unequally Spaced Observations.
Bibliography.
Index.
