Spatial Statistics and Spatio-Temporal Data : Covariance Functions and Directional Properties.

By: Sherman, MichaelContributor(s): Li, BoMaterial type: TextTextSeries: Wiley Series in Probability and Statistics SerPublisher: New York : John Wiley & Sons, Incorporated, 2010Copyright date: ©2010Edition: 1st edDescription: 1 online resource (296 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780470974407Subject(s): Analysis of covariance | Spatial analysis (Statistics)Genre/Form: Electronic books.Additional physical formats: Print version:: Spatial Statistics and Spatio-Temporal Data : Covariance Functions and Directional PropertiesDDC classification: 519.5 LOC classification: QA278.2 -- .S497 2010ebOnline resources: Click to View
Contents:
Intro -- Spatial Statistics and Spatio-Temporal Data -- Contents -- Preface -- 1 Introduction -- 1.1 Stationarity -- 1.2 The effect of correlation in estimation and prediction -- 1.2.1 Estimation -- 1.2.2 Prediction -- 1.3 Texas tidal data -- 2 Geostatistics -- 2.1 A model for optimal prediction and error assessment -- 2.2 Optimal prediction (kriging) -- 2.2.1 An example: phosphorus prediction -- 2.2.2 An example in the power family of variogram functions -- 2.3 Prediction intervals -- 2.3.1 Predictions and prediction intervals for lognormal observations -- 2.4 Universal kriging -- 2.4.1 Optimal prediction in universal kriging -- 2.5 The intuition behind kriging -- 2.5.1 An example: the kriging weights in the phosphorus data -- 3 Variogram and covariance models and estimation -- 3.1 Empirical estimation of the variogram or covariance function -- 3.1.1 Robust estimation -- 3.1.2 Kernel smoothing -- 3.2 On the necessity of parametric variogram and covariance models -- 3.3 Covariance and variogram models -- 3.3.1 Spectral methods and the Matérn covariance model -- 3.4 Convolution methods and extensions -- 3.4.1 Variogram models where no covariance function exists -- 3.4.2 Jumps at the origin and the nugget effect -- 3.5 Parameter estimation for variogram and covariance models -- 3.5.1 Estimation with a nonconstant mean function -- 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 -- 4.1.1 A data example: model fitting for the wheat yield data -- 4.2 Estimation for binary spatial observations -- 4.2.1 Edge effects -- 4.2.2 Goodness of model fit -- 5 Isotropy -- 5.1 Geometric anisotropy -- 5.2 Other types of anisotropy -- 5.3 Covariance modeling under anisotropy -- 5.4 Detection of anisotropy: the rose plot.
5.5 Parametric methods to assess isotropy -- 5.6 Nonparametric methods of assessing anisotropy -- 5.6.1 Regularly spaced data case -- 5.6.2 Irregularly spaced data case -- 5.6.3 Choice of spatial lags for assessment of isotropy -- 5.6.4 Test statistics -- 5.6.5 Numerical results -- 5.7 Assessment of isotropy for general sampling designs -- 5.7.1 A stochastic sampling design -- 5.7.2 Covariogram estimation and asymptotic properties -- 5.7.3 Testing for spatial isotropy -- 5.7.4 Numerical results for general spatial designs -- 5.7.5 Effect of bandwidth and block size choice -- 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-temporal prediction -- 6.3 Empirical estimation of the variogram, covariance models, and estimation -- 6.3.1 Space-time symmetry and separability -- 6.4 Spatio-temporal covariance models -- 6.4.1 Nonseparable space-time covariance models -- 6.5 Space-time models -- 6.6 Parametric methods of assessing full symmetry and space-time separability -- 6.7 Nonparametric methods of assessing full symmetry and space-time separability -- 6.7.1 Irish wind data -- 6.7.2 Pacific Ocean wind data -- 6.7.3 Numerical experiments based on the Irish wind data -- 6.7.4 Numerical experiments on the test for separability for data on a grid -- 6.7.5 Taylor's hypothesis -- 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 -- 8.4.1 Poisson cluster processes -- 8.4.2 Simple inhibition processes -- 8.5 An application to leukemia data.
9 Multivariate spatial and spatio-temporal models -- 9.1 Cokriging -- 9.2 An alternative to cokriging -- 9.2.1 Statistical model -- 9.2.2 Model fitting -- 9.2.3 Prediction -- 9.2.4 Validation -- 9.3 Multivariate covariance functions -- 9.3.1 Variogram function or covariance function? -- 9.3.2 Intrinsic correlation, separable models -- 9.3.3 Coregionalization and kernel convolution models -- 9.4 Testing and assessing intrinsic correlation -- 9.4.1 Testing procedures for intrinsic correlation and symmetry -- 9.4.2 Determining the order of a linear model of coregionalization -- 9.4.3 Covariance estimation -- 9.5 Numerical experiments -- 9.5.1 Symmetry -- 9.5.2 Intrinsic correlation -- 9.5.3 Linear model of coregionalization -- 9.6 A data application to pollutants -- 9.7 Discussion -- 10 Resampling for correlated observations -- 10.1 Independent observations -- 10.1.1 U-statistics -- 10.1.2 The jackknife -- 10.1.3 The bootstrap -- 10.2 Other data structures -- 10.3 Model-based bootstrap -- 10.3.1 Regression -- 10.3.2 Time series: autoregressive models -- 10.4 Model-free resampling methods -- 10.4.1 Resampling for stationary dependent observations -- 10.4.2 Block bootstrap -- 10.4.3 Block jackknife -- 10.4.4 A numerical experiment -- 10.5 Spatial resampling -- 10.5.1 Model-based resampling -- 10.5.2 Monte Carlo maximum likelihood -- 10.6 Model-free spatial resampling -- 10.6.1 A spatial numerical experiment -- 10.6.2 Spatial bootstrap -- 10.7 Unequally spaced observations -- Bibliography -- Index.
Summary: In the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent and more established methods are illustrated to assess many common assumptions on these functions, such as, isotropy, separability, symmetry, and intrinsic correlation. After an extensive introduction to spatial methodology, the book details the effects of common covariance assumptions and addresses methods to assess the appropriateness of such assumptions for various data structures. Key features: An extensive introduction to spatial methodology including a survey of spatial covariance functions and their use in spatial prediction (kriging) is given. Explores methodology for assessing the appropriateness of assumptions on covariance functions in the spatial, spatio-temporal, multivariate spatial, and point pattern settings. Provides illustrations of all methods based on data and simulation experiments to demonstrate all methodology and guide to proper usage of all methods. Presents a brief survey of spatial and spatio-temporal models, highlighting the Gaussian case and the binary data setting, along with the different methodologies for estimation and model fitting for these two data structures. Discusses models that allow for anisotropic and nonseparable behaviour in covariance functions in the spatial, spatio-temporal and multivariate settings. Gives an introduction to point pattern models, including testing for randomness, and fitting regular and clustered point patterns. The importance and assessment of isotropy of point patterns is detailed. Statisticians, researchers, and data analysts workingSummary: with spatial and space-time data will benefit from this book as well as will graduate students with a background in basic statistics following courses in engineering, quantitative ecology or atmospheric science.
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Intro -- Spatial Statistics and Spatio-Temporal Data -- Contents -- Preface -- 1 Introduction -- 1.1 Stationarity -- 1.2 The effect of correlation in estimation and prediction -- 1.2.1 Estimation -- 1.2.2 Prediction -- 1.3 Texas tidal data -- 2 Geostatistics -- 2.1 A model for optimal prediction and error assessment -- 2.2 Optimal prediction (kriging) -- 2.2.1 An example: phosphorus prediction -- 2.2.2 An example in the power family of variogram functions -- 2.3 Prediction intervals -- 2.3.1 Predictions and prediction intervals for lognormal observations -- 2.4 Universal kriging -- 2.4.1 Optimal prediction in universal kriging -- 2.5 The intuition behind kriging -- 2.5.1 An example: the kriging weights in the phosphorus data -- 3 Variogram and covariance models and estimation -- 3.1 Empirical estimation of the variogram or covariance function -- 3.1.1 Robust estimation -- 3.1.2 Kernel smoothing -- 3.2 On the necessity of parametric variogram and covariance models -- 3.3 Covariance and variogram models -- 3.3.1 Spectral methods and the Matérn covariance model -- 3.4 Convolution methods and extensions -- 3.4.1 Variogram models where no covariance function exists -- 3.4.2 Jumps at the origin and the nugget effect -- 3.5 Parameter estimation for variogram and covariance models -- 3.5.1 Estimation with a nonconstant mean function -- 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 -- 4.1.1 A data example: model fitting for the wheat yield data -- 4.2 Estimation for binary spatial observations -- 4.2.1 Edge effects -- 4.2.2 Goodness of model fit -- 5 Isotropy -- 5.1 Geometric anisotropy -- 5.2 Other types of anisotropy -- 5.3 Covariance modeling under anisotropy -- 5.4 Detection of anisotropy: the rose plot.

5.5 Parametric methods to assess isotropy -- 5.6 Nonparametric methods of assessing anisotropy -- 5.6.1 Regularly spaced data case -- 5.6.2 Irregularly spaced data case -- 5.6.3 Choice of spatial lags for assessment of isotropy -- 5.6.4 Test statistics -- 5.6.5 Numerical results -- 5.7 Assessment of isotropy for general sampling designs -- 5.7.1 A stochastic sampling design -- 5.7.2 Covariogram estimation and asymptotic properties -- 5.7.3 Testing for spatial isotropy -- 5.7.4 Numerical results for general spatial designs -- 5.7.5 Effect of bandwidth and block size choice -- 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-temporal prediction -- 6.3 Empirical estimation of the variogram, covariance models, and estimation -- 6.3.1 Space-time symmetry and separability -- 6.4 Spatio-temporal covariance models -- 6.4.1 Nonseparable space-time covariance models -- 6.5 Space-time models -- 6.6 Parametric methods of assessing full symmetry and space-time separability -- 6.7 Nonparametric methods of assessing full symmetry and space-time separability -- 6.7.1 Irish wind data -- 6.7.2 Pacific Ocean wind data -- 6.7.3 Numerical experiments based on the Irish wind data -- 6.7.4 Numerical experiments on the test for separability for data on a grid -- 6.7.5 Taylor's hypothesis -- 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 -- 8.4.1 Poisson cluster processes -- 8.4.2 Simple inhibition processes -- 8.5 An application to leukemia data.

9 Multivariate spatial and spatio-temporal models -- 9.1 Cokriging -- 9.2 An alternative to cokriging -- 9.2.1 Statistical model -- 9.2.2 Model fitting -- 9.2.3 Prediction -- 9.2.4 Validation -- 9.3 Multivariate covariance functions -- 9.3.1 Variogram function or covariance function? -- 9.3.2 Intrinsic correlation, separable models -- 9.3.3 Coregionalization and kernel convolution models -- 9.4 Testing and assessing intrinsic correlation -- 9.4.1 Testing procedures for intrinsic correlation and symmetry -- 9.4.2 Determining the order of a linear model of coregionalization -- 9.4.3 Covariance estimation -- 9.5 Numerical experiments -- 9.5.1 Symmetry -- 9.5.2 Intrinsic correlation -- 9.5.3 Linear model of coregionalization -- 9.6 A data application to pollutants -- 9.7 Discussion -- 10 Resampling for correlated observations -- 10.1 Independent observations -- 10.1.1 U-statistics -- 10.1.2 The jackknife -- 10.1.3 The bootstrap -- 10.2 Other data structures -- 10.3 Model-based bootstrap -- 10.3.1 Regression -- 10.3.2 Time series: autoregressive models -- 10.4 Model-free resampling methods -- 10.4.1 Resampling for stationary dependent observations -- 10.4.2 Block bootstrap -- 10.4.3 Block jackknife -- 10.4.4 A numerical experiment -- 10.5 Spatial resampling -- 10.5.1 Model-based resampling -- 10.5.2 Monte Carlo maximum likelihood -- 10.6 Model-free spatial resampling -- 10.6.1 A spatial numerical experiment -- 10.6.2 Spatial bootstrap -- 10.7 Unequally spaced observations -- Bibliography -- Index.

In the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent and more established methods are illustrated to assess many common assumptions on these functions, such as, isotropy, separability, symmetry, and intrinsic correlation. After an extensive introduction to spatial methodology, the book details the effects of common covariance assumptions and addresses methods to assess the appropriateness of such assumptions for various data structures. Key features: An extensive introduction to spatial methodology including a survey of spatial covariance functions and their use in spatial prediction (kriging) is given. Explores methodology for assessing the appropriateness of assumptions on covariance functions in the spatial, spatio-temporal, multivariate spatial, and point pattern settings. Provides illustrations of all methods based on data and simulation experiments to demonstrate all methodology and guide to proper usage of all methods. Presents a brief survey of spatial and spatio-temporal models, highlighting the Gaussian case and the binary data setting, along with the different methodologies for estimation and model fitting for these two data structures. Discusses models that allow for anisotropic and nonseparable behaviour in covariance functions in the spatial, spatio-temporal and multivariate settings. Gives an introduction to point pattern models, including testing for randomness, and fitting regular and clustered point patterns. The importance and assessment of isotropy of point patterns is detailed. Statisticians, researchers, and data analysts working

with spatial and space-time data will benefit from this book as well as will graduate students with a background in basic statistics following courses in engineering, quantitative ecology or atmospheric science.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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