Statistical methods for spatial data analysis

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
1 Introduction
	1.1 The Need for Spatial Analysis
	1.2 Types of Spatial Data
		1.2.1 Geostatistical Data
		1.2.2 Lattice Data, Regional Data
		1.2.3 Point Patterns
	1.3 Autocorrelation—Concept and Elementary Measures
		1.3.1 Mantel’s Tests for Clustering
		1.3.2 Measures on Lattices
		1.3.3 Localized Indicators of Spatial Autocorrelation
	1.4 Autocorrelation Functions
		1.4.1 The Autocorrelation Function of a Time Series
		1.4.2 Autocorrelation Functions in Space—Covariance and Semivariogram
		1.4.3 From Mantel’s Statistic to the Semivariogram
	1.5 The Effects of Autocorrelation on Statistical Inference
		1.5.1 Effects on Prediction
		1.5.2 Effects on Precision of Estimators
	1.6 Chapter Problems
2 Some Theory on Random Fields
	2.1 Stochastic Processes and Samples of Size One
	2.2 Stationarity, Isotropy, and Heterogeneity
	2.3 Spatial Continuity and Differentiability
	2.4 Random Fields in the Spatial Domain
		2.4.1 Model Representation
		2.4.2 Convolution Representation
	2.5 Random Fields in the Frequency Domain
		2.5.1 Spectral Representation of Deterministic Functions
		2.5.2 Spectral Representation of Random Processes
		2.5.3 Covariance and Spectral Density Function
		2.5.4 Properties of Spectral Distribution Functions
		2.5.5 Continuous and Discrete Spectra
		2.5.6 Linear Location-Invariant Filters
		2.5.7 Importance of Spectral Analysis
	2.6 Chapter Problems
3 Mapped Point Patterns
	3.1 Random, Aggregated, and Regular Patterns
	3.2 Binomial and Poisson Processes
		3.2.1 Bernoulli and Binomial Processes
		3.2.2 Poisson Processes
		3.2.3 Process Equivalence
	3.3 Testing for Complete Spatial Randomness
		3.3.1 Monte Carlo Tests
		3.3.2 Simulation Envelopes
		3.3.3 Tests Based on Quadrat Counts
		3.3.4 Tests Based on Distances
	3.4 Second-Order Properties of Point Patterns
		3.4.1 The Reduced Second Moment Measure— The K-Function
		3.4.2 Estimation of K- and L-Functions
		3.4.3 Assessing the Relationship between Two Patterns
	3.5 The Inhomogeneous Poisson Process
		3.5.1 Estimation of the Intensity Function
		3.5.2 Estimating the Ratio of Intensity Functions
		3.5.3 Clustering and Cluster Detection
	3.6 Marked and Multivariate Point Patterns
		3.6.1 Extensions
		3.6.2 Intensities and Moment Measures for Multivariate Point Patterns
	3.7 Point Process Models
		3.7.1 Thinning and Clustering
		3.7.2 Clustered Processes
		3.7.3 Regular Processes
	3.8 Chapter Problems
4 Semivariogram and Covariance Function Analysis and Estimation
	4.1 Introduction
	4.2 Semivariogram and Covariogram
		4.2.1 Definition and Empirical Counterparts
		4.2.2 Interpretation as Structural Tools
	4.3 Covariance and Semivariogram Models
		4.3.1 Model Validity
		4.3.2 The Matérn Class of Covariance Functions
		4.3.3 The Spherical Family of Covariance Functions
		4.3.4 Isotropic Models Allowing Negative Correlations
		4.3.5 Basic Models Not Second-Order Stationary
		4.3.6 Models with Nugget Effects and Nested Models
		4.3.7 Accommodating Anisotropy
	4.4 Estimating the Semivariogram
		4.4.1 Matheron’s Estimator
		4.4.2 The Cressie-Hawkins Robust Estimator
		4.4.3 Estimators Based on Order Statistics and Quantiles
	4.5 Parametric Modeling
		4.5.1 Least Squares and the Semivariogram
		4.5.2 Maximum and Restricted Maximum Likelihood
		4.5.3 Composite Likelihood and Generalized Estimating Equations
		4.5.4 Comparisons
	4.6 Nonparametric Estimation and Modeling
		4.6.1 The Spectral Approach
		4.6.2 The Moving-Average Approach
		4.6.3 Incorporating a Nugget Effect
	4.7 Estimation and Inference in the Frequency Domain
		4.7.1 The Periodogram on a Rectangular Lattice
		4.7.2 Spectral Density Functions
		4.7.3 Analysis of Point Patterns
	4.8 On the Use of Non-Euclidean Distances in Geostatistics
		4.8.1 Distance Metrics and Isotropic Covariance Functions
		4.8.2 Multidimensional Scaling
	4.9 Supplement: Bessel Functions
		4.9.1 Bessel Function of the First Kind
		4.9.2 Modified Bessel Functions of the First and Second Kind
	4.10 Chapter Problems
5 Spatial Prediction and Kriging
	5.1 Optimal Prediction in Random Fields
	5.2 Linear Prediction—Simple and Ordinary Kriging
		5.2.1 The Mean Is Known—Simple Kriging
		5.2.2 The Mean Is Unknown and Constant—Ordinary Kriging
		5.2.3 Effects of Nugget, Sill, and Range
	5.3 Linear Prediction with a Spatially Varying Mean
		5.3.1 Trend Surface Models
		5.3.2 Localized Estimation
		5.3.3 Universal Kriging
	5.4 Kriging in Practice
		5.4.1 On the Uniqueness of the Decomposition
		5.4.2 Local Versus Global Kriging
		5.4.3 Filtering and Smoothing
	5.5 Estimating Covariance Parameters
		5.5.1 Least Squares Estimation
		5.5.2 Maximum Likelihood
		5.5.3 Restricted Maximum Likelihood
		5.5.4 Prediction Errors When Covariance Parameters Are Estimated
	5.6 Nonlinear Prediction
		5.6.1 Lognormal Kriging
		5.6.2 Trans-Gaussian Kriging
		5.6.3 Indicator Kriging
		5.6.4 Disjunctive Kriging
	5.7 Change of Support
		5.7.1 Block Kriging
		5.7.2 The Multi-Gaussian Approach
		5.7.3 The Use of Indicator Data
		5.7.4 Disjunctive Kriging and Isofactorial Models
		5.7.5 Constrained Kriging
	5.8 On the Popularity of the Multivariate Gaussian Distribution
	5.9 Chapter Problems
6 Spatial Regression Models
	6.1 Linear Models with Uncorrelated Errors
		6.1.1 Ordinary Least Squares—Inference and Diagnostics
		6.1.2 Working with OLS Residuals
		6.1.3 Spatially Explicit Models
	6.2 Linear Models with Correlated Errors
		6.2.1 Mixed Models
		6.2.2 Spatial Autoregressive Models
		6.2.3 Generalized Least Squares—Inference and Diagnostics
	6.3 Generalized Linear Models
		6.3.1 Background
		6.3.2 Fixed Effects and the Marginal Specification
		6.3.3 A Caveat
		6.3.4 Mixed Models and the Conditional Specification
		6.3.5 Estimation in Spatial GLMs and GLMMs
		6.3.6 Spatial Prediction in GLMs
	6.4 Bayesian Hierarchical Models
		6.4.1 Prior Distributions
		6.4.2 Fitting Bayesian Models
		6.4.3 Selected Spatial Models
	6.5 Chapter Problems
7 Simulation of Random Fields
	7.1 Unconditional Simulation of Gaussian Random Fields
		7.1.1 Cholesky (LU) Decomposition
		7.1.2 Spectral Decomposition
	7.2 Conditional Simulation of Gaussian Random Fields
		7.2.1 Sequential Simulation
		7.2.2 Conditioning a Simulation by Kriging
	7.3 Simulated Annealing
	7.4 Simulating from Convolutions
	7.5 Simulating Point Processes
		7.5.1 Homogeneous Poisson Process on the Rectangle (0,0)× (a,b) with Intensity λ
		7.5.2 Inhomogeneous Poisson Process with Intensity λ(s)
	7.6 Chapter Problems
8 Non-Stationary Covariance
	8.1 Types of Non-Stationarity
	8.2 Global Modeling Approaches
		8.2.1 Parametric Models
		8.2.2 Space Deformation
	8.3 Local Stationarity
		8.3.1 Moving Windows
		8.3.2 Convolution Methods
		8.3.3 Weighted Stationary Processes
9 Spatio-Temporal Processes
	9.1 A New Dimension
	9.2 Separable Covariance Functions
	9.3 Non-Separable Covariance Functions
		9.3.1 Monotone Function Approach
		9.3.2 Spectral Approach
		9.3.3 Mixture Approach
		9.3.4 Differential Equation Approach
	9.4 The Spatio-Temporal Semivariogram
	9.5 Spatio-Temporal Point Processes
		9.5.1 Types of Processes
		9.5.2 Intensity Measures
		9.5.3 Stationarity and Complete Randomness
References
Author Index
Subject Index