Spatial Analysis. Kanti V. Mardia

      

      Table of Contents

      1  Cover

      2  Title Page

      3  Copyright

      4  Dedication

      5  Dedication

      6  List of Figures

      7  List of Tables

      8  Preface

      9  List of Notation and Terminology

      10  1 Introduction 1.1 Spatial Analysis 1.2 Presentation of the Data 1.3 Objectives 1.4 The Covariance Function and Semivariogram 1.5 Behavior of the Sample Semivariogram 1.6 Some Special Features of Spatial Analysis Exercises

      11  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 2.9 Smoothness 2.10 Regularization 2.11 Lattice Random Fields 2.12 Torus Models 2.13 Long‐range Correlation 2.14 Simulation Exercises

      12  3 Intrinsic and Generalized Random Fields 3.1 Introduction 3.2 Intrinsic Random Fields of Order

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

3.8 Spectral Theory for Intrinsic and Generalized Processes 3.9 Regularization for Intrinsic and Generalized Processes 3.10 Self‐Similarity 3.11 Simulation 3.12 Dispersion Variance Exercises

      13  4 Autoregression and Related Models 4.1 Introduction 4.2 Background 4.3 Moving Averages 4.4 Finite Symmetric Neighborhoods of the Origin in

4.5 Simultaneous Autoregressions (SARs) 4.6 Conditional Autoregressions (CARs) 4.7 Limits of CAR Models Under Fine Lattice Spacing 4.8 Unilateral Autoregressions for Lattice Random Fields 4.9 Markov Random Fields (MRFs) 4.10 Markov Mesh Models Exercises

      14  5 Estimation of Spatial Structure 5.1 Introduction 5.2 Patterns of Behavior 5.3 Preliminaries 5.4 Exploratory and Graphical Methods 5.5 Maximum Likelihood for Stationary Models 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