Spatial Analysis. Kanti V. Mardia

Spatial Linear Model 5.12 REML for the Spatial Linear Model 5.13 Intrinsic Random Fields 5.14 Infill Asymptotics and Fractal Dimension Exercises

      15  6 Estimation for Lattice Models 6.1 Introduction 6.2 Sample Moments 6.3 The AR(1) Process on

6.4 Moment Methods for Lattice Data 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

      16  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 7.7 Stationary Examples 7.8 Intrinsic Random Fields 7.9 Intrinsic Examples 7.10 Square Example 7.11 Kriging with Derivative Information 7.12 Bayesian Kriging 7.13 Kriging and Machine Learning 7.14 The Link Between Kriging and Splines 7.15 Reproducing Kernel Hilbert Spaces 7.16 Deformations Exercises

      17  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 8.7 Clamped Plate Splines 8.8 Gaussian Markov Random Field Approximations 8.9 Designing a Monitoring Network Exercises

      18  Appendix A Mathematical Background A.1 Domains for Sequences and Functions A.2 Classes of Sequences and Functions A.3 Matrix Algebra 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.8 Discrete Cosine Transform (DCT) A.9 Periodic Approximations to Sequences A.10 Structured Matrices in

Dimension A.11 Matrix Approximations for an Inverse Covariance Matrix A.12 Maximum Likelihood Estimation A.13 Bias in Maximum Likelihood Estimation

      19  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.4 Frequentist vs. Bayesian Inference

      20  References and Author Index

      21  Index

      22  Wiley End User License Agreement

      List of Tables

      1 Chapter 1Table 1.1 Illustrative data

, on a

regular grid, represented in various ...Table 1.2 Elevation data: elevation

in feet above the sea level, where

,...Table 1.3 Bauxite data: percentage