Statistícal Methods for Spatial Data Analysis

Transcription

1 Texts in Statistícal Science Statistícal Methods for Spatial Data Analysis V- Oliver Schabenberger Carol A. Gotway PCT CHAPMAN & K

2 Contents Preface xv 1 Introduction The Need for Spatial Analysis Types of Spatial Data Geostatistical Data Lattice Data, Regional Data Point Patterns Autocorrelation Concept and Elementary Measures Mantel's Tests for Clustering Measures on Lattices Localized Indicators of Spatial Autocorrelation Autocorrelation Functions The Autocorrelation Function of a Time Series Autocorrelation Functions in Space Covariance and Semivariogram From Mantel's Statistic to the Semivariogram The Effects of Autocorrelation on Statistical Inference Effects on Prediction Effects on Precisión of Estimators Chapter Problems 37 2 Some Theory on Random Fields Stochastic Processes and Samples of Size One Stationarity, Isotropy, and Heterogeneity Spatial Continuity and Differentiability Random Fields in the Spatial Domain Model Representation Convolution Representation Random Fields in the Frequency Domain Spectral Representation of Deterministic Functions Spectral Representation of Random Processes Covariance and Spectral Density Function Properties of Spectral Distribution Functions Continuous and Discrete Spectra Linear Location-Invariant Filters 74

3 x CONTENTS Importance of Spectral Analysis Chapter Problems 78 3 Mapped Point Patterns Random, Aggregated, and Regular Patterns Binornial and Poisson Processes Bernoulli and Binomial Processes Poisson Processes Process Equivalence Testing for Complete Spatial Randomness Monte Cario Tests Simulation Envelopes Tests Based on Quadrat Counts Tests Based on Distances Second-Order Properties of Point Patterns The Reduced Second Moment Measure The K-Function Estimation of K- and L-Functions Assessing the Relationship between Two Patterns The Inhomogeneous Poisson Process Estimation of the Intensity Function Estimating the Ratio of Intensity Functions Clustering and Cluster Detection Marked and Multivariate Point Patterns Extensions Intensities and Moment Measures for Multivariate Point Patterns Point Process Models Thinning and Clustering Clustered Processes Regular Processes Chapter Problems 129 Semivariogram and Covariance Function Analysis and Estimation Introduction Semivariogram and Covariogram Defmition and Empirical Counterparts Interpretation as Structural Tools Covariance and Semivariogram Models Model Validity The Matérn Class of Covariance Functions The Spherical Family of Covariance Functions Isotropic Models Allowing Negative Correlations Basic Models Not Second-Order Stationary Models with Nugget Effects and Nested Models 150

4 4.3.7 Accommodating Anisotropy Estimating the Semivariogram Matheron's Estimator The Cressie-Hawkins Robust Estimator Estiraators Based on Order Statistics and Quantiles Parametric Modeling Least Squares and the Semivariogram Máximum and Restricted Máximum Likelihood Composite Likelihood and Generalized Estimating Equations Comparisons Nonparametric Estimation and Modeling The Spectral Approach The Moving-Average Approach Incorporating a Nugget Effect Estimation and Inference in the Frequency Domain The Periodogram on a Rectangular Lattice Spectral Density Functions Analysis of Point Patterns On the Use of Non-Euclidean Distances in Geostatistics Distance Metrics and Isotropic Covariance Functions Multidimensional Scaling Supplement: Bessel Functions Bessel Function of the First Kind Modified Bessel Functions of the First and Second Kind Chapter Problems 211 Spatial Prediction and Kriging Optimal Prediction in Random Fields Linear Prediction Simple and Ordinary Kriging The Mean Is Known Simple Kriging The Mean Is Unknown and Constant Ordinary Kriging Effects of Nugget, Sill, and Range Linear Prediction with a Spatially Varying Mean Trend Surface Models Localized Estimation Universal Kriging Kriging in Practice On the Uniqueness of the Decomposition Local Versus Global Kriging Filtering and Smoothing Estimating Covariance Parameters Least Squares Estimation Máximum Likelihood Restricted Máximum Likelihood 261

5 xii CONTENTS Prediction Errors When Covariance Parameters Are Estimated Nonlinear Prediction Lognormal Kriging Trans-Gaussian Kriging Indicator Kriging Disjunctive Kriging Change of Support Block Kriging The Multi-Gaussian Approach The Use of Indicator Data Disjunctive Kriging and Isofactorial Models Constrained Kriging On the Popularity of the Multivariate Gaussian Distribution Chapter Problems Spatial Regression Models Linear Models with Uncorrelated Errors Ordinary Least Squares Inference and Diagnostics Working with OLS Residuals Spatially Explicit Models Linear Models with Correlated Errors Mixed Models Spatial Autoregressive Models Generalizad Least Squares Inference and Diagnostics Generalized Linear Models Background Fixed Effects and the Marginal Specification A Caveat Mixed Models and the Conditional Specification Estimation in Spatial GLMs and GLMMs Spatial Prediction in GLMs Bayesian Hierarchical Models Prior Distributions Fitting Bayesian Models Selected Spatial Models Chapter Problems Simulation of Random Fields Unconditional Simulation of Gaussian Random Fields Cholesky (LU) Decomposition Spectral Decomposition Conditional Simulation of Gaussian Random Fields Sequential Simulation Conditioning a Simulation by Kriging Simulated Annealing 409

6 7.4 Simulating from Convolutions Simulating Point Processes Homogeneous Poisson Process on the Rectangle (0,0) x (a, 6) with Intensity A Inhomogeneous Poisson Process with Intensity A(s) Chapter Problems Non-Stationary Covariance Types of Non-Stationarity Global Modeling Approaches Parametric Models Space Deformation Local Stationarity Moving Windows Convolution Methods Weighted Stationary Processes Spatio-Temporal Processes A New Dimensión Separable Covariance Functions Non-Separable Covariance Functions Monotone Function Approach Spectral Approach Mixture Approach Differential Equation Approach The Spatio-Temporal Semivariogram Spatio-Temporal Point Processes Types of Processes Intensity Measures Stationarity and Complete Randomness 444 References 447 Author Index 463 i, Subject Index 467