Statistical Methods for Spatial Data Analysis: 1st Edition (e-Book) book cover

Statistical Methods for Spatial Data Analysis

1st Edition

By Oliver Schabenberger, Carol A. Gotway

Chapman and Hall/CRC

512 pages | 81 B/W Illus.

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pub: 2004-12-20
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Description

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.

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

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

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
TEC036000
TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems