Statistical Methods for Spatial Data Analysis

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ISBN 9781584883227
Cat# C3227



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  • Provides a treatment of basic statistical theory and methods for spatial data analysis
  • Offers statistical tools for the analysis of mapped point patterns
  • Includes a comprehensive section on spatial analysis in the spectral domain
  • Gives an up-to-date treatment of semivariogram estimation and modeling
  • Includes a statistical treatment of geostatistical methods for spatial prediction
  • Provides a thorough treatment of the theory and methods for spatial regression analysis including model diagnostics for linear and generalized linear spatial models and spline smoothing with mixed models
  • Reviews Bayesian hierarchical models for spatial data, simulation of random fields, non-stationary covariance and spatio-temporal processes
  • Provides both theoretical and practical problems at the end of the main chapters for use as a graduate-level textbook
  • Summary

    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

    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

    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

    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 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

    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

    Linear Models with Uncorrelated Errors
    Linear Models with Correlated Errors
    Generalized Linear Models
    Bayesian Hierarchical Models
    Chapter Problems

    Unconditional Simulation of Gaussian Random Fields
    Conditional Simulation of Gaussian Random Fields
    Simulated Annealing
    Simulating from Convolutions
    Simulating Point Processes
    Chapter Problems

    Types of Non-Stationarity
    Global Modeling Approaches
    Local Stationarity

    A New Dimension
    Separable Covariance Functions
    Non-Separable Covariance Functions
    The Spatio-Temporal Semivariogram
    Spatio-Temporal Point Processes

    Editorial Reviews

    "…well-presented research-level text with interesting examples and an extensive reference list, much of which relates to work which has appeared during the last five years or so."
    International Statistics Institute, 2005

    "This book tackles spatial data analysis from a statistician's point of view. It provides a very natural bridge to spatial data analysis for the classically trained statistician who is familiar with linear models and the like. In terms of detail, it is at a very good level for its stated audience of a graduate class in spatial statistics; there is much useful information….The authors have made a tightly written and well-planned contribution that updates much relevant material and provides welcome and thoughtful advice. …I have no hesitation in recommending it for a graduate class in spatial statistics, and it is a welcome addition to my library."
    -Journal of the Royal Statistical Society, Series A, Andrew Robinson, University of Melbourne

    "This book provides an introduction to statistical methods for the analysis of spatial data. In a coherent manner, it presents statistical tools and approaches for analysis of three types of spatial data: geostatistical data, lattice data, and point patterns. …The book is intended as a text for a graduate-level course in spatial statistics. I believe that it would be a suitable text for a variety of reasons. First of all, the book provides comprehensive coverage of statistical methods for geostatistical data, lattice data, and point patterns. Not many books on spatial statistics have this feature. …The book has a nice balance of statistical theory, methodology, and applications, with an emphasis on statistical methods. It contains many concrete examples that illustrate both theory and methods. In illustrating the methods, real and interesting data examples are drawn from many disciplines such as agriculture, ecology, geology, epidemiology, and meteorology. …This is a wonderful book that systematically introduces readers to spatial statistics. With a writing style that is illustrative, clear, thoughtful, and cogent, teachers and students alike should find it a delightful text for this diverse and exciting field."
    -Journal of the American Statistical Association, Jun Zhu, University of Wisconsin-Madison

    "I enjoyed this book and I am sure that it is a valuable addition to the literature which should be widely read."

    – Stelios Zimeras, University of the Aegean, in Journal of Applied Statistics, Jan 2008, Vol. 35, No. 1

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