Statistical Methods for Spatial Data Analysis: (Chapman & Hall/CRC Texts in Statistical Science)

Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.

Table of Contents:
INTRODUCTION The Need for Spatial Analysis Types of Spatial Data Autocorrelation-Concept and Elementary Measures Autocorrelation Functions The Effects of Autocorrelation on Statistical Inference Chapter Problems 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 Random Fields in the Frequency Domain Chapter Problems MAPPED POINT PATTERNS Random, Aggregated, and Regular Patterns Binomial and Poisson Processes Testing for Complete Spatial Randomness Second-Order Properties of Point Patterns The Inhomogeneous Poisson Process Marked and Multivariate Point Patterns Point Process Models Chapter Problems SEMIVARIOGRAM AND COVARIANCE FUNCTION ANALYSIS AND ESTIMATION Introduction Semivariogram and Covariogram Covariance and Semivariogram Models Estimating the Semivariogram Parametric Modeling Nonparametric Estimation and Modeling Estimation and Inference in the Frequency Domain On the Use of Non-Euclidean Distances in Geostatistics Supplement: Bessel Functions Chapter Problems SPATIAL PREDICTION AND KRIGING Optimal Prediction in Random Fields Linear Prediction-Simple and Ordinary Kriging Linear Prediction with a Spatially Varying Mean Kriging in Practice Estimating Covariance Parameters Nonlinear Prediction Change of Support On the Popularity of the Multivariate Gaussian Distribution Chapter Problems SPATIAL REGRESSION MODELS Linear Models with Uncorrelated Errors Linear Models with Correlated Errors Generalized Linear Models Bayesian Hierarchical Models Chapter Problems SIMULATION OF RANDOM FIELDS Unconditional Simulation of Gaussian Random Fields Conditional Simulation of Gaussian Random Fields Simulated Annealing Simulating from Convolutions Simulating Point Processes Chapter Problems NON-STATIONARY COVARIANCE Types of Non-Stationarity Global Modeling Approaches Local Stationarity SPATIO-TEMPORAL PROCESSES A New Dimension Separable Covariance Functions Non-Separable Covariance Functions The Spatio-Temporal Semivariogram Spatio-Temporal Point Processes