Hierarchical Modeling and Analysis for Spatial Data
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Summary
Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis, or written at a level often inaccessible to those lacking a strong background in mathematical statistics.
Hierarchical Modeling and Analysis for Spatial Data is the first accessible, self-contained treatment of hierarchical methods, modeling, and data analysis for spatial and spatio-temporal data. Starting with overviews of the types of spatial data, the data analysis tools appropriate for each, and a brief review of the Bayesian approach to statistics, the authors discuss hierarchical modeling for univariate spatial response data, including Bayesian kriging and lattice (areal data) modeling. They then consider the problem of spatially misaligned data, methods for handling multivariate spatial responses, spatio-temporal models, and spatial survival models. The final chapter explores a variety of special topics, including spatially varying coefficient models.
This book provides clear explanations, plentiful illustrations --some in full color--a variety of homework problems, and tutorials and worked examples using some of the field's most popular software packages.. Written by a team of leaders in the field, it will undoubtedly remain the primary textbook and reference on the subject for years to come.
Table of Contents
OVERVIEW OF SPATIAL DATA PROBLEMS
Introduction to Spatial Data and Models
Fundamentals of Cartography
Exercises
BASICS OF POINT-REFERENCED DATA MODELS
Elements of Point-Referenced Modeling
Spatial Process Models
Exploratory Approaches for Point-Referenced Data
Classical Spatial Prediction
Computer Tutorials
Exercises
BASICS OF AREAL DATA MODELS
Exploratory Approaches for Areal Data
Brook's Lemma and Markov Random Fields
Conditionally Autoregressive (CAR) Models
Simultaneous Autoregressive (SAR) Models
Computer Tutorials
Exercises
BASICS OF BAYESIAN INFERENCE
Introduction to Hierarchical Modeling and Bayes Theorem
Bayesian Inference
Bayesian Computation
Computer Tutorials
Exercises
HIERARCHICAL MODELING FOR UNIVARIATE SPATIAL DATA
Stationary Spatial Process Models
Generalized Linear Spatial Process Modeling
Nonstationary Spatial Process Models
Areal Data Models
General Linear Areal Data Modeling
Exercises
SPATIAL MISALIGNMENT
Point-Level Modeling
Nested Block-Level Modeling
Nonnested Block-Level Modeling
Misaligned Regression Modeling
Exercises
MULTIVARIATE SPATIAL MODELING
Separable Models
Coregionalization Models
Other Constructive Approaches
Multivariate Models for Areal Data
Exercises
SPATIOTEMPORAL MODELING
General Modeling Formulation
Point-Level Modeling with Continuous Time
Nonseparable Spatio-Temporal Models
Dynamic Spatio-Temporal Models
Block-Level Modeling
Exercises
SPATIAL SURVIVAL MODELS
Parametric Models
Semiparametric Models
Spatio-Temporal Models
Multivariate Models
Spatial Cure Rate Models
Exercises
SPECIAL TOPICS IN SPATIAL PROCESS MODELING
Process Smoothness Revisited
Spatially Varying Coefficient Models
Spatial CDFs
APPENDICES
Matrix Theory and Spatial Computing Methods
Answers to Selected Exercises
REFERENCES
AUTHOR INDEX
SUBJECT INDEX
Short TOC
Editorial Reviews
"This book was a pleasure to review. Most of the emphasis is on insight and intuition with relatively little on traditional multivariate techniques. I also found some of the explanations delightful…[W]hile they did not convert me to Bayesianism, [the authors] made me reconsider some of my assumptions. They later state 'Our book is intended as a research monograph, presenting the state of the art' and my impression is that they have succeeded…In many sections the formulae are augmented by showing R or S code, making it easy to actually apply the mathematics. In summary, this is a nice book."
-Short Book Reviews of the International Statistical Institute
"The book contains a wealth of material not available elsewhere in a unified manner. Each chapter contains worked out examples using some well known software packages and has exercises with related computer code and data on a supporting web page. The book is up to date in its coverage…an important addition to the literature on spatial data analysis."
-Zentralblatt MATH 1053
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