1.frontmatter

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© 2010 by Taylor and Francis Group, LLC


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Handbook of spatial statistics / [edited by] Alan E. Gelfand … [et al.].

p. cm. -- (Chapman & Hall/CRC handbooks of modern statistical methods)

Includes bibliographical references and index.

ISBN 978-1-4200-7287-7 (hardcover : alk. paper)

1. Spatial analysis (Statistics) 2. Mathematical statistics--Methodology. I. Gelfand, Alan E., 1945-

II. Title. III. Series.

QA278.2.H374 2010

519.5--dc22 2010006620

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi

Part I Introduction

1. Historical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Peter J. Diggle

Part II Continuous Spatial Variation

2. Continuous Parameter Stochastic Process Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Tilmann Gneiting and Peter Guttorp

3. Classical Geostatistical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Dale L. Zimmerman and Michael Stein

4. Likelihood-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45Dale L. Zimmerman

5. Spectral Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Montserrat Fuentes and Brian Reich

6. Asymptotics for Spatial Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Michael Stein

7. Hierarchical Modeling with Spatial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89Christopher K. Wikle

8. Low-Rank Representations for Spatial Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107Christopher K. Wikle

9. Constructions for Nonstationary Spatial Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Paul D. Sampson

10. Monitoring Network Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131James V. Zidek and Dale L. Zimmerman

11. Non-Gaussian and Nonparametric Models for Continuous Spatial Data . . . . . . . 149Mark F.J. Steel and Montserrat Fuentes

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vi Contents

Part III Discrete Spatial Variation

12. Discrete Spatial Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Havard Rue and Leonhard Held

13. Conditional and Intrinsic Autoregressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Leonhard Held and Havard Rue

14. Disease Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Lance Waller and Brad Carlin

15. Spatial Econometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245R. Kelley Pace and James LeSage

Part IV Spatial Point Patterns

16. Spatial Point Process Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Marie-Colette van Lieshout

17. Spatial Point Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283Valerie Isham

18. Nonparametric Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299Peter J. Diggle

19. Parametric Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Jesper Møller

20. Modeling Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339Adrian Baddeley

21. Multivariate and Marked Point Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371Adrian Baddeley

22. Point Process Models and Methods in Spatial Epidemiology . . . . . . . . . . . . . . . . . . .403Lance Waller

Part V Spatio-Temporal Processes

23. Continuous Parameter Spatio-Temporal Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427Tilmann Gneiting and Peter Guttorp

24. Dynamic Spatial Models Including Spatial Time Series . . . . . . . . . . . . . . . . . . . . . . . .437Dani Gamerman

25. Spatio-Temporal Point Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449Peter J. Diggle and Edith Gabriel


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Contents vii

26. Modeling Spatial Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463David R. Brillinger

27. Data Assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477Douglas W. Nychka and Jeffrey L. Anderson

Part VI Additional Topics

28. Multivariate Spatial Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495Alan E. Gelfand and Sudipto Banerjee

29. Misaligned Spatial Data: The Change of Support Problem . . . . . . . . . . . . . . . . . . . . . 517Alan E. Gelfand

30. Spatial Aggregation and the Ecological Fallacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .541Jonathan Wakefield and Hilary Lyons

31. Spatial Gradients and Wombling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .559Sudipto Banerjee

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577


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Preface

Spatial statistics has an unusual history as a field within the discipline of statistics. Thestochastic process theory that underlies much of the field was developed within the math-ematical sciences by probabilists, whereas, early on, much of the statistical methodologywas developed quite independently. In fact, this methodology grew primarily from thedifferent areas of application, including mining engineering, which led to the develop-ment of geostatistics by Matheron and colleagues; agriculture with spatial considerationsinformed by the thinking of Fisher on randomization and blocking; and forestry, whichwas the setting for the seminal PhD thesis of Matern. As a result, for many years spatialstatistics labored on the fringe of mainstream statistics. However, the past 20 years hasseen an explosion of interest in space and space–time problems. This has been largely fu-eled by the increased availability of inexpensive, high-speed computing (as has been thecase for many other areas). Such availability has enabled the collection of large spatial andspatio-temporal datasets across many fields, has facilitated the widespread usage of sophis-ticated geographic information systems (GIS) software to create attractive displays, and hasendowed the ability to investigate (fit and infer under) challenging, evermore appropriateand realistic models.

In the process, spatial statistics has been brought into the mainstream of statistical researchwith a proliferation of books (including this one), conferences and workshops, as well ascourses and short courses. Moreover, while there has been a body of strong theoreticalwork developed since the 1950s (Whittle, Bartlett, Besag, etc.), it is safe to say that, broadly,spatial statistics has been changed from a somewhat ad hoc field to a more model-drivenone. Though the entire field continues to be in flux, we, as editors taking on this project,feel that it is now mature enough to warrant a handbook. In this regard, we hope that thisvolume will serve as a worthy successor to Noel Cressie’s (1993) encyclopedic effort, whichhas served as the “handbook” since its publication. However, this observation further arguesthe need for a new handbook. In addition to a dramatic increase in size since Cressie’s bookappeared, the literature has become exceptionally diverse, in part due to the diversity ofapplications. Collecting a review of the major portion of this work in one place, with anextensive bibliography, should certainly assist future research in the field.

Spatial statistics is generally viewed as being comprised of three major branches: (1) con-tinuous spatial variation, i.e., point referenced data; (2) discrete spatial variation, includinglattice and areal unit data; and (3) spatial point patterns. However, this handbook consistsof 31 chapters spread over six sections. Our rationale is as follows. The three main areasform the subject matter of Parts II, III and IV, respectively, and span the majority of the book.However, we felt that a historical introduction detailing the aforementioned evolution ofthe field would be valuable. In addition, with so much space–time work being available,it was clear that a section on this material was needed. Finally, as anticipated with sucha project, we needed an “Additional Topics” section to collect some important topics thatbuild upon material presented in the earlier sections, but, in some sense, seemed beyondthose earlier ones. We acknowledge that some readers will feel that certain topics are under-represented or inadequately discussed. We cannot disagree, noting only that no selectionwould make all readers happy.

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x Preface

The list of contributors to this volume is outstanding, a collection of very prominentresearchers in the field. Moreover, we have attempted to give the handbook a more unified,integrated feel. We specifically precluded the notion of stand-alone contributions. Rather, foreach chapter, the editors provided the contributor(s) with a core set of material to be coveredas well as chapter reviews, which reinforced this. In addition, though there is inherent vari-ability in technical levels across the chapters, we have targeted a background/preparationat the level of a master’s in statistics. We hope that this will make the book accessible to re-searchers in many other fields, researchers seeking an easy entry to particular topics. In thisregard, we have tried to balance theory and application while targeting a strong emphasison modeling and introducing as many real data analysis examples as feasible.

We have focused a bit less on computation (though there are some exceptions) and not atall on GIS displays and software (arguing that this is primarily descriptive). In this spirit,we have also avoided discussion of what is often referred to as spatial analysis becausethis work resides primarily in the geography literature and does not tend to be stochastic.However, with regard to computing issues, typically, there is some discussion in mostof the nontheoretical chapters. We also decided not to say much about available softwarepackages. In our view, the material we have included is perceived as durable, while softwarefor spatial and spatio-temporal analysis is evolving rapidly and is perhaps best pursuedthrough appropriate references cited in the volume.

In summary, we have enjoyed assembling this handbook, finding collegial ease andconsistent agreement across the editorial team. We greatly appreciate the efforts of ourcontributors who provided their chapters and their revisions in a timely manner to enablethis book to come together with minimal delay. And, we appreciate the encouragement ofRob Calver from Taylor & Francis to undertake this project and Sarah Morris and MarshaPronin, also from T&F, who helped put the entire package together.

Alan E. Gelfand

Peter J. Diggle

Montserrat Fuentes

Peter Guttorp


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List of Contributors

Jeffrey L. AndersonNational Center for Atmospheric ResearchBoulder, Colorado

Adrian BaddeleyCSIRO Mathematical and Information

SciencesPerth, Western AustraliaandSchool of Mathematics and StatisticsUniversity of Western AustraliaCrawley, Western Australia

Sudipto BanerjeeSchool of Public HealthUniversity of MinnesotaMinneapolis, Minnesota

David R. BrillingerDepartment of StatisticsUniversity of CaliforniaBerkeley, California

Brad CarlinDivision of BiostatisticsSchool of Public HealthUniversity of MinnesotaMinneapolis, Minnesota

Peter J. DiggleDivision of MedicineLancaster UniversityLancaster, United Kingdom

Montserrat FuentesDepartment of StatisticsNorth Carolina State UniversityRaleigh, North Carolina

Edith GabrielIUT, Departement STIDUniversity of AvignonAvignon, France

Dani GamermanInstituto de Matematica – UFRJRio de Janeiro, Brazil

Alan E. GelfandDepartment of Statistical ScienceDuke UniversityDurham, North Carolina

Tilmann GneitingInstitut fur Angewandte MathematikUniversitat HeidelbergHeidelberg, Germany

Peter GuttorpDepartment of StatisticsUniversity of WashingtonSeattle, Washington

Leonhard HeldBiostatistics UnitInstitute of Social and Preventive

MedicineUniversity of ZurichZurich, Switzerland

Valerie IshamDepartment of Statistical ScienceUniversity College LondonLondon, United Kingdom

James LesageDepartment of Finance and EconomicsMcCoy College of Business

AdministrationTexas State University – San MarcosSan Marcos, Texas

Hilary LyonsDepartment of StatisticsUniversity of WashingtonSeattle, Washington

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List of Contributors xii

Jesper MøllerDepartment of Mathematical SciencesAalborg UniversityAalborg, Denmark

Douglas W. NychkaNational Center for Atmospheric ResearchBoulder, Colorado

Kelley PaceDepartment of FinanceE.J. Ourso College of BusinessLouisiana State UniversityBaton Rouge, Louisiana

Havard RueDepartment of Mathematical SciencesNorwegian University of Science

and TechnologyTrondheim, Norway

Paul D. SampsonDepartment of StatisticsUniversity of WashingtonSeattle, Washington

Mark SteelDepartment of StatisticsUniversity of WarwickCoventry, United Kingdom

Michael SteinDepartment of StatisticsUniversity of ChicagoChicago, Illinois

Marie-Colette van LieshoutProbability and Stochastic

Networks (PNA2)Amsterdam, the Netherlands

Jonathan WakefieldDepartments of Statistics and BiostatisticsUniversity of WashingtonSeattle, Washington

Lance WallerRollins School of Public HealthEmory UniversityAtlanta, Georgia

Chris WikleDepartment of StatisticsUniversity of MissouriColumbia, Missouri

Jim ZidekDepartment of StatisticsUniversity of British ColumbiaVancouver, British Columbia, Canada

Dale ZimmermanDepartment of Statistics

and Actuarial ScienceUniversity of IowaIowa City, Iowa

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1.frontmatter

Documents