Spatial analysis / / John T. Kent, Kanti V. Mardia

• Autore: Kent J. T (John T.)
• Pubblicazione: Hoboken, New Jersey : , : Wiley, , [2022]; ©2022
• Descrizione fisica: 1 online resource (403 pages)
• Disciplina: 001.422
• Soggetto topico: Spatial analysis (Statistics)
• Persona (resp. second.): MardiaK. V.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Title Page -- Copyright -- Contents -- List of Figures -- List of Tables -- Preface -- List of Notation and Terminology -- Chapter 1 Introduction -- 1.1 Spatial Analysis -- 1.2 Presentation of the Data -- 1.3 Objectives -- 1.4 The Covariance Function and Semivariogram -- 1.4.1 General Properties -- 1.4.2 Regularly Spaced Data -- 1.4.3 Irregularly Spaced Data -- 1.5 Behavior of the Sample Semivariogram -- 1.6 Some Special Features of Spatial Analysis -- Exercises -- Chapter 2 Stationary Random Fields -- 2.1 Introduction -- 2.2 Second Moment Properties -- 2.3 Positive Definiteness and the Spectral Representation -- 2.4 Isotropic Stationary Random Fields -- 2.5 Construction of Stationary Covariance Functions -- 2.6 Matérn Scheme -- 2.7 Other Examples of Isotropic Stationary Covariance Functions -- 2.8 Construction of Nonstationary Random Fields -- 2.8.1 Random Drift -- 2.8.2 Conditioning -- 2.9 Smoothness -- 2.10 Regularization -- 2.11 Lattice Random Fields -- 2.12 Torus Models -- 2.12.1 Models on the Continuous Torus -- 2.12.2 Models on the Lattice Torus -- 2.13 Long‐range Correlation -- 2.14 Simulation -- 2.14.1 General Points -- 2.14.2 The Direct Approach -- 2.14.3 Spectral Methods -- 2.14.4 Circulant Methods -- Exercises -- Chapter 3 Intrinsic and Generalized Random Fields -- 3.1 Introduction -- 3.2 Intrinsic Random Fields of Order k& -- equals -- 0 -- 3.3 Characterizations of Semivariograms -- 3.4 Higher Order Intrinsic Random Fields -- 3.5 Registration of Higher Order Intrinsic Random Fields -- 3.6 Generalized Random Fields -- 3.7 Generalized Intrinsic Random Fields of Intrinsic Order k≥0 -- 3.8 Spectral Theory for Intrinsic and Generalized Processes -- 3.9 Regularization for Intrinsic and Generalized Processes -- 3.10 Self‐Similarity -- 3.11 Simulation -- 3.11.1 General Points -- 3.11.2 The Direct Method -- 3.11.3 Spectral Methods. ; 3.12 Dispersion Variance -- Exercises -- Chapter 4 Autoregression and Related Models -- 4.1 Introduction -- 4.2 Background -- 4.3 Moving Averages -- 4.3.1 Lattice Case -- 4.3.2 Continuously Indexed Case -- 4.4 Finite Symmetric Neighborhoods of the Origin in Zd -- 4.5 Simultaneous Autoregressions (SARs) -- 4.5.1 Lattice Case -- 4.5.2 Continuously Indexed Random Fields -- 4.6 Conditional Autoregressions (CARs) -- 4.6.1 Stationary CARs -- 4.6.2 Iterated SARs and CARs -- 4.6.3 Intrinsic CARs -- 4.6.4 CARs on a Lattice Torus -- 4.6.5 Finite Regions -- 4.7 Limits of CAR Models Under Fine Lattice Spacing -- 4.8 Unilateral Autoregressions for Lattice Random Fields -- 4.8.1 Half‐spaces in Zd -- 4.8.2 Unilateral Models -- 4.8.3 Quadrant Autoregressions -- 4.9 Markov Random Fields (MRFs) -- 4.9.1 The Spatial Markov Property -- 4.9.2 The Subset Expansion of the Negative Potential Function -- 4.9.3 Characterization of Markov Random Fields in Terms of Cliques -- 4.9.4 Auto‐models -- 4.10 Markov Mesh Models -- 4.10.1 Validity -- 4.10.2 Marginalization -- 4.10.3 Markov Random Fields -- 4.10.4 Usefulness -- Exercises -- Chapter 5 Estimation of Spatial Structure -- 5.1 Introduction -- 5.2 Patterns of Behavior -- 5.2.1 One‐dimensional Case -- 5.2.2 Two‐dimensional Case -- 5.2.3 Nugget Effect -- 5.3 Preliminaries -- 5.3.1 Domain of the Spatial Process -- 5.3.2 Model Specification -- 5.3.3 Spacing of Data -- 5.4 Exploratory and Graphical Methods -- 5.5 Maximum Likelihood for Stationary Models -- 5.5.1 Maximum Likelihood Estimates - Known Mean -- 5.5.2 Maximum Likelihood Estimates - Unknown Mean -- 5.5.3 Fisher Information Matrix and Outfill Asymptotics -- 5.6 Parameterization Issues for the Matérn Scheme -- 5.7 Maximum Likelihood Examples for Stationary Models -- 5.8 Restricted Maximum Likelihood (REML) -- 5.9 Vecchia's Composite Likelihood. ; 5.10 REML Revisited with Composite Likelihood -- 5.11 Spatial Linear Model -- 5.11.1 MLEs -- 5.11.2 Outfill Asymptotics for the Spatial Linear Model -- 5.12 REML for the Spatial Linear Model -- 5.13 Intrinsic Random Fields -- 5.14 Infill Asymptotics and Fractal Dimension -- Exercises -- Chapter 6 Estimation for Lattice Models -- 6.1 Introduction -- 6.2 Sample Moments -- 6.3 The AR(1) Process on Z -- 6.4 Moment Methods for Lattice Data -- 6.4.1 Moment Methods for Unilateral Autoregressions (UARs) -- 6.4.2 Moment Estimators for Conditional Autoregression (CAR) Models -- 6.5 Approximate Likelihoods for Lattice Data -- 6.6 Accuracy of the Maximum Likelihood Estimator -- 6.7 The Moment Estimator for a CAR Model -- Exercises -- Chapter 7 Kriging -- 7.1 Introduction -- 7.2 The Prediction Problem -- 7.3 Simple Kriging -- 7.4 Ordinary Kriging -- 7.5 Universal Kriging -- 7.6 Further Details for the Universal Kriging Predictor -- 7.6.1 Transfer Matrices -- 7.6.2 Projection Representation of the Transfer Matrices -- 7.6.3 Second Derivation of the Universal Kriging Predictor -- 7.6.4 A Bordered Matrix Equation for the Transfer Matrices -- 7.6.5 The Augmented Matrix Representation of the Universal Kriging Predictor -- 7.6.6 Summary -- 7.7 Stationary Examples -- 7.8 Intrinsic Random Fields -- 7.8.1 Formulas for the Kriging Predictor and Kriging Variance -- 7.8.2 Conditionally Positive Definite Matrices -- 7.9 Intrinsic Examples -- 7.10 Square Example -- 7.11 Kriging with Derivative Information -- 7.12 Bayesian Kriging -- 7.12.1 Overview -- 7.12.2 Details for Simple Bayesian Kriging -- 7.12.3 Details for Bayesian Kriging with Drift -- 7.13 Kriging and Machine Learning -- 7.14 The Link Between Kriging and Splines -- 7.14.1 Nonparametric Regression -- 7.14.2 Interpolating Splines -- 7.14.3 Comments on Interpolating Splines -- 7.14.4 Smoothing Splines. ; 7.15 Reproducing Kernel Hilbert Spaces -- 7.16 Deformations -- Exercises -- Chapter 8 Additional Topics -- 8.1 Introduction -- 8.2 Log‐normal Random Fields -- 8.3 Generalized Linear Spatial Mixed Models (GLSMMs) -- 8.4 Bayesian Hierarchical Modeling and Inference -- 8.5 Co‐kriging -- 8.6 Spatial-temporal Models -- 8.6.1 General Considerations -- 8.6.2 Examples -- 8.7 Clamped Plate Splines -- 8.8 Gaussian Markov Random Field Approximations -- 8.9 Designing a Monitoring Network -- Exercises -- Appendix A Mathematical Background -- A.1 Domains for Sequences and Functions -- A.2 Classes of Sequences and Functions -- A.2.1 Functions on the Domain Rd -- A.2.2 Sequences on the Domain Zd -- A.2.3 Classes of Functions on the Domain S1d -- A.2.4 Classes of Sequences on the Domain ZNd, Where N& -- equals -- (n[1],…,n[d]) -- A.3 Matrix Algebra -- A.3.1 The Spectral Decomposition Theorem -- A.3.2 Moore-Penrose Generalized Inverse -- A.3.3 Orthogonal Projection Matrices -- A.3.4 Partitioned Matrices -- A.3.5 Schur Product -- A.3.6 Woodbury Formula for a Matrix Inverse -- A.3.7 Quadratic Forms -- A.3.8 Toeplitz and Circulant Matrices -- A.3.9 Tensor Product Matrices -- A.3.10 The Spectral Decomposition and Tensor Products -- A.3.11 Matrix Derivatives -- A.4 Fourier Transforms -- A.5 Properties of the Fourier Transform -- A.6 Generalizations of the Fourier Transform -- A.7 Discrete Fourier Transform and Matrix Algebra -- A.7.1 DFT in d& -- equals -- 1 Dimension -- A.7.2 Properties of the Unitary Matrix G, d& -- equals -- 1 -- A.7.3 Circulant Matrices and the DFT, d& -- equals -- 1 -- A.7.4 The Case d> -- 1 -- A.7.5 The Periodogram -- A.8 Discrete Cosine Transform (DCT) -- A.8.1 One‐dimensional Case -- A.8.2 The Case d> -- 1 -- A.8.3 Indexing for the Discrete Fourier and Cosine Transforms -- A.9 Periodic Approximations to Sequences. ; A.10 Structured Matrices in d& -- equals -- 1 Dimension -- A.11 Matrix Approximations for an Inverse Covariance Matrix -- A.11.1 The Inverse Covariance Function -- A.11.2 The Toeplitz Approximation to Σ−1 -- A.11.3 The Circulant Approximation to Σ−1 -- A.11.4 The Folded Circulant Approximation to Σ−1 -- A.11.5 Comments on the Approximations -- A.11.6 Sparsity -- A.12 Maximum Likelihood Estimation -- A.12.1 General Considerations -- A.12.2 The Multivariate Normal Distribution and the Spatial Linear Model -- A.12.3 Change of Variables -- A.12.4 Profile Log‐likelihood -- A.12.5 Confidence Intervals -- A.12.6 Linked Parameterization -- A.12.7 Model Choice -- A.13 Bias in Maximum Likelihood Estimation -- A.13.1 A General Result -- A.13.2 The Spatial Linear Model -- Appendix B A Brief History of the Spatial Linear Model and the Gaussian Process Approach -- B.1 Introduction -- B.2 Matheron and Watson -- B.3 Geostatistics at Leeds 1977-1987 -- B.3.1 Courses, Publications, Early Dissemination -- B.3.2 Numerical Problems with Maximum Likelihood -- B.4 Frequentist vs. Bayesian Inference -- References and Author Index -- Index -- EULA.
• Titolo autorizzato: Spatial analysis
• ISBN: 1-118-76356-4; 1-118-76355-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910585794703321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley Series in Probability and Statistics Ser.