Statistics for Spatial Data

The Wiley Classics Library consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. Spatial statistics — analyzing spatial data through statistical models — has proven exceptionally versatile, encompassing problems ranging from the microscopic to the astronomic. However, for the scientist and engineer faced only with scattered and uneven treatments of the subject in the scientific literature, learning how to make practical use of spatial statistics in day-to-day analytical work is very difficult. Designed exclusively for scientists eager to tap into the enormous potential of this analytical tool and upgrade their range of technical skills, Statistics for Spatial Data is a comprehensive, single-source guide to both the theory and applied aspects of spatial statistical methods. The hard-cover edition was hailed by Mathematical Reviews as an "excellent book which will become a basic reference." This paper-back edition of the 1993 edition, is designed to meet the many technological challenges facing the scientist and engineer. Concentrating on the three areas of geostatistical data, lattice data, and point patterns, the book sheds light on the link between data and model, revealing how design, inference, and diagnostics are an outgrowth of that link. It then explores new methods to reveal just how spatial statistical models can be used to solve important problems in a host of areas in science and engineering. Discussion includes: Exploratory spatial data analysis Spectral theory for stationary processes Spatial scale Simulation methods for spatial processes Spatial bootstrapping Statistical image analysis and remote sensing Computational aspects of model fitting Application of models to disease mapping Designed to accommodate the practical needs of the professional, it features a unified and common notation for its subject as well as many detailed examples woven into the text, numerous illustrations (including graphs that illuminate the theory discussed) and over 1,000 references. Fully balancing theory with applications, Statistics for Spatial Data, Revised Edition is an exceptionally clear guide on making optimal use of one of the ascendant analytical tools of the decade, one that has begun to capture the imagination of professionals in biology, earth science, civil, electrical, and agricultural engineering, geography, epidemiology, and ecology.

Table of Contents:
Preface xv Acknowledgments xix 1. Statistics for Spatial Data 1 1.1 Spatial Data and Spatial Models, 7 1.2 Introductory Examples, 10 1.2.1 Geostatistical Data, 10 1.2.2 Lattice Data, 11 1.2.3 Point Patterns, 12 1.3 Statistics for Spatial Data: Why?, 13 PART I GEOSTATISTICAL DATA 2. Geostatistics 2.1 Continuous Spatial Index, 29 2.2+ Spatial Data Analysis of Coal Ash in Pennsylvania, 30 2.2.1* Intrinsic Stationarity, 40 2.2.2* Square-Root-Differences Cloud, 41 2.2.3* The Pocket Plot, 42 2.2.4* Decomposing the Data into Large- and Small-Scale Variation, 46 2.2.5* Analysis of Residuals, 48 2.2.6* Variogram of Residuals from Median Polish, 50 2.3* Stationary Processes, 52 2.3.1 Variogram, 58 2.3.2 Covariogram and Correlogram, 67 2.4 Estimation of the Variogram, 69 2.4.1 Comparison of Variogram and Covariogram Estimation, 70 2.4.2 Exact Distribution Theory for the Variogram Estimator, 73 2.4.3 Robust Estimation of the Variogram, 74 2.5* Spectral Representations, 83 2.5.1* Valid Covariograms, 84 2.5.2* Valid Variograms, 86 2.6 Variogram Model Fitting, 90 2.6.1 Criteria for Fitting a Variogram Model, 91 2.6.2 Least Squares, 94 2.6.3 Properties of Variogram-Parameter Estimators, 99 2.6.4 Cross-Validating the Fitted Variogram, 101 3 Spatial Prediction and Kriging 105 3.1 Scale of Variation, 112 3.2 Ordinary Kriging, 119 3.2.1 Effect of Variogram Parameters on Kriging, 127 3.2.2 Lognormal and Trans-Gaussian Kriging, 135 3.2.3 Cokriging, 138 3.2.4 Some Final Remarks, 142 3.3 Robust Kriging, 144 3.4 Universal Kriging, 151 3.4.1 Universal Kriging of Coal-Ash Data, 157 3.4.2 Trend-Surface Prediction, 162 3.4.3 Estimating the Variogram for Universal Kriging, 165 3.4.4 Bayesian Kriging, 170 3.4.5 Kriging Revisited, 172 3.5 Median-Polish Kriging, 183 3.5.1 Gridded Data, 184 3.5.2 Nongridded Data, 193 3.5.3 Median Polishing Spatial Data: Inference Results, 194 3.5.4 Median-Based Covariogram Estimators are Less Biased, 196 3.6 Geostatistical Data, Simulated and Real, 200 3.6.1 Simulation of Spatial Processes, 201 3.6.2 Conditional Simulation, 207 3.6.3 Geostatistical Data, 209 4. Applications of Geostatistics 4.1* Wolfcamp-Aquifer Data, 212 4.1.1* Intrinsic-Stationarity Assumption, 213 4.1.2* Nonconstant-Mean Assumption, 217 4.2* Soil-Water Tension Data, 224 4.3* Soil-Water-Infiltration Data, 230 4.3.1* Estimating and Modeling the Spatial Dependence, 232 4.3.2* Inference on Mean Effects (Spatial Analysis of Variance), 238 4.4* Sudden-Infant-Death-Syndrome Data, 244 4.5* Wheat-Yield Data, 248 4.5.1* Presence of Trend in the Data, 250 4.5.2* Intrinsic Stationarity, 251 4.5.3* Median-Polish (Robust) Kriging, 255 4.6* Acid-Deposition Data, 259 4.6.1* Spatial Modeling and Prediction, 260 4.6.2* Sampling Design, 268 4.7 Space-Time Geostatistical Data, 273 5. Special Topics in Statistics for Spatial Data 277 5.1* Nonlinear Geostatistics, 278 5.2 Change of Support, 284 5.3 Stability of the Geostatistical Method, 289 5.3.1 Estimation of Spatial-Dependence Parameters, 291 5.3.2 Stability of the Kriging Predictor, 292 5.3.3 Stability of the Kriging Variance, 296 5.4 Intrinsic Random Functions of Order k, 299 5.5* Applications of the Theory of Random Processes, 309 5.6 Spatial Design, 313 5.6.1 Spatial Sampling Design, 314 5.6.2* Spatial Experimental Design, 324 5.7 Field Trials, 338 5.7.1 Nearest-Neighbor Analyses, 338 5.7.2 Analyses Based on Spatial Modeling, 344 5.8 Infill Asymptotics, 350 5.9 The Many Faces of Spatial Prediction, 356 5.9.1 Stochastic Methods of Spatial Prediction, 357 5.9.2 Nonstochastic Methods of Spatial Prediction, 370 5.9.3 Comparisons and Some Final Remarks, 378 PART II LATTICE DATA 6. Spatial Models on Lattices 383 6.1 Lattices, 383 6.2* Spatial Data Analysis of Sudden Infant Deaths in North Carolina, 385 6.2.1* Nonspatial Data Analysis, 391 6.2.2* Spatial Data Analysis, 393 6.2.3* Trend Removal, 396 6.2.4* Some Final Remarks, 401 6.3 Conditionally and Simultaneously Specified Spatial Gaussian Models, 402 6.3.1 Simultaneously Specified Spatial Gaussian Models, 405 6.3.2 Conditionally Specified Spatial Gaussian Models, 407 6.3.3 Comparison, 408 6.4* Markov Random Fields, 410 6.4.1* Neighbors, Cliques, and the Negpotential Function Q, 414 6.4.2* Pairwise-Only Dependence and Conditional Exponential Distributions, 419 6.4.3* Some Final Remarks, 422 6.5 Conditionally Specified Spatial Models for Discrete Data, 423 6.5.1 Binary Data, 423 6.5.2 Counts Data, 427 6.6 Conditionally Specified Spatial Models for Continuous Data, 433 6.7 Simultaneously Specified and Other Spatial Models, 440 6.7.1 Simultaneously Specified Spatial Models, 440 6.7.2 Other Spatial Models, 447 6.8 Space-Time Models, 449 7. Inference for Lattice Models 453 7.1* Inference for the Mercer and Hall Wheat-Yield Data, 453 7.1.1* Data Description, 454 7.1.2* Spatial Lattice Models, 456 7.2 Parameter Estimation for Lattice Models, 458 7.2.1 Estimation Criteria, 458 7.2.2 Gaussian Maximum Likelihood Estimation, 465 7.2.3 Some Computational Details, 472 7.3 Properties of Estimators, 477 7.3.1* Increasing-Domain Asymptotics, 480 7.3.2 The Jackknife and Bootstrap for Spatial Lattice Data, 489 7.3.3 Cross-Validation and Model Selection, 497 7.4 Statistical Image Analysis and Remote Sensing, 499 7.4.1 Remote Sensing, 501 7.4.2 Ordinary Discriminant Analysis, 502 7.4.3* Markov-Random-Field Models, 509 7.4.4* Edge Processes, 521 7.4.5* Textured Images, 525 7.4.6* Single Photon Emission Tomography, 525 7.4.7* Least Squares and Image Regularization, 528 7.4.8* Method of Sieves, 532 7.4.9* Mathematical Morphology, 534 7.5 Regional Mapping, Scotland Lip-Cancer Data, 535 7.5.1* Exploratory Regional Mapping, 537 7.5.2 Parametric Empirical Bayes Mapping, 544 7.6 Sudden-Infant-Death-Syndrome Data, 548 7.6.1* Exploratory Spatial Data Analysis, 549 7.6.2 Auto-Poisson Model, 553 7.6.3 Auto-Gaussian Model, 555 7.7 Lattice Data, Simulated and Real, 568 7.7.1 Simulation of Lattice Processes, 569 7.7.2 Lattice Data, 572 PART III SPATIAL PATTERNS 8. Spatial Point Patterns 577 8.1 Random Spatial Index, 578 8.2 Spatial Data Analysis of Longleaf Pines (Pinus palustris), 579 8.2.1* Data Description, 579 8.2.2 Complete Spatial Randomness, Regularity, and Clustering, 580 8.2.3* Quadrat Methods, 588 8.2.4* Kernel Estimators of the Intensity Function, 597 8.2.5* Distance Methods, 602 8.2.6* Nearest-Neighbor Distribution Functions and the Κ Function, 613 8.2.7* Some Final Remarks, 618 8.3* Point Process Theory, 619 8.3.1* Moment Measures, 622 8.3.2* Generating Functionals, 624 8.3.3* Stationary and Isotropic Point Processes, 628 8.3.4* Palm Distributions, 630 8.3.5* Reduced Second Moment Measure, 631 8.4 Complete Spatial Randomness, Distance Functions, and Second Moment Measures, 633 8.4.1 Complete Spatial Randomness, 633 8.4.2 Distance Functions, 636 8.4.3 Κ Functions, 639 8.4.4f Animal-Behavior Data, 644 8.4.5 Some Final Remarks, 649 8.5 Models and Model Fitting, 650 8.5.1* Inhomogeneous Poisson Process, 650 8.5.2* Cox Process, 657 8.5.3* Poisson Cluster Process, 661 8.5.4* Simple Inhibition Point Processes, 669 8.5.5* Markov Point Process, 673 8.5.6* Thinned and Related Point Processes, 689 8.5.7* Other Models, 693 8.5.8* Some Final Remarks, 694 8.6* Multivariate Spatial Point Processes, 696 8.6.1* Theoretical Considerations, 696 8.6.2* Estimation of the Cross Κ Function, 698 8.6.3* Bivariate Spatial-Point-Process Models, 699 8.7* Marked Spatial Point Processes, 707 8.7.1* Theoretical Considerations, 707 8.7.2* Estimation of Moment Measures, 714 8.7.3* Marked Spatial-Point-Process Models, 716 8.8 Space-Time Point Patterns, 719 8.9 Spatial Point Patterns, Simulated and Real, 722 8.9.1 Simulation of Spatial Point Patterns, 722 8.9.2 Spatial Point Patterns, 723 9. Modeling Objects 725 9.1 Set Models, 727 9.1.1 Fractal Sets, 727 9.1.2 Fuzzy Sets, 731 9.1.3 Random Closed Sets: An Example, 736 9.2f Random Parallelograms in IR2, 739 9.3* Random Closed Sets and Mathematical Morphology, 742 9.3.1* Theory and Methods, 745 9.3.2* Inference on Random Closed Sets, 750 9.4 The Boolean Model, 753 9.4.1* Main Properties, 755 9.4.2* Generalizations of the Boolean Model, 756 9.5 Methods of Boolean-Model Parameter Estimation, 759 9.5.1 Analysis of Random-Parallelograms Data, 761 9.5.2 Analysis of Heather-Incidence Data, 763 9.5.3* Intensity Estimation in the Boolean Model, 765 9.6 Inference for the Boolean Model, 770 9.7 Modeling Growth with Random Sets, 776 9.7.1 Random-Set Growth Models, 777 9.7.2 Tumor-Growth Data, 783 9.7.3 Fitting the Tumor-Growth Parameters, 794 References 803 Author Index 873 Subject Index 887