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Statistics for Spatio-Temporal Data


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Table of Contents

Preface xv Acknowledgments xix 1 Space?Time: The Next Frontier 1 2 Statistical Preliminaries 17 2.1 Conditional Probabilities and Hierarchical Modeling (HM), 20 2.2 Inference and Diagnostics, 33 2.3 Computation of the Posterior Distribution, 42 2.4 Graphical Representations of Statistical Dependencies, 48 2.5 Data/Model/Computing Compromises, 53 3 Fundamentals of Temporal Processes 55 3.1 Characterization of Temporal Processes, 56 3.2 Introduction to Deterministic Dynamical Systems, 59 3.3 Time Series Preliminaries, 80 3.4 Basic Time Series Models, 84 3.5 Spectral Representation of Temporal Processes, 100 3.6 Hierarchical Modeling of Time Series, 112 3.7 Bibliographic Notes, 116 4 Fundamentals of Spatial Random Processes 119 4.1 Geostatistical Processes, 124 4.2 Lattice Processes, 167 4.3 Spatial Point Processes, 204 4.4 Random Sets, 224 4.5 Bibliographic Notes, 231 5 Exploratory Methods for Spatio-Temporal Data 243 5.1 Visualization, 244 5.2 Spectral Analysis, 259 5.3 Empirical Orthogonal Function (EOF) Analysis, 266 5.4 Extensions of EOF Analysis, 271 5.5 Principal Oscillation Patterns (POPs), 279 5.6 Spatio-Temporal Canonical Correlation Analysis (CCA), 284 5.7 Spatio-Temporal Field Comparisons, 291 5.8 Bibliographic Notes, 292 6 Spatio-Temporal Statistical Models 297 6.1 Spatio-Temporal Covariance Functions, 304 6.2 Spatio-Temporal Kriging, 321 6.3 Stochastic Differential and Difference Equations, 327 6.4 Time Series of Spatial Processes, 336 6.5 Spatio-Temporal Point Processes, 347 6.6 Spatio-Temporal Components-of-Variation Models, 351 6.7 Bibliographic Notes, 356 7 Hierarchical Dynamical Spatio-Temporal Models 361 7.1 Data Models for the DSTM, 363 7.2 Process Models for the DSTM: Linear Models, 382 7.3 Process Models for the DSTM: Nonlinear Models, 403 7.4 Process Models for the DSTM: Multivariate Models, 418 7.5 DSTM Parameter Models, 425 7.6 Dynamical Design of Monitoring Networks, 430 7.7 Switching the Emphasis of Time and Space, 432 7.8 Bibliographic Notes, 433 8 Hierarchical DSTMs: Implementation and Inference 441 8.1 DSTM Process: General Implementation and Inference, 441 8.2 Inference for the DSTM Process: Linear/Gaussian Models, 444 8.3 Inference for the DSTM Parameters: Linear/Gaussian Models, 450 8.4 Inference for the Hierarchical DSTM: Nonlinear/Non-Gaussian Models, 460 8.5 Bibliographic Notes, 472 9 Hierarchical DSTMs: Examples 475 9.1 Long-Lead Forecasting of Tropical Pacific Sea Surface Temperatures, 476 9.2 Remotely Sensed Aerosol Optical Depth, 488 9.3 Modeling and Forecasting the Eurasian Collared Dove Invasion, 499 9.4 Mediterranean Surface Vector Winds, 507 Epilogue 519 References 523 Index 571

About the Author

Noel Cressie, PhD, is Professor of Statistics and Directorof the Program in Spatial Statistics and Environmental Statisticsat The Ohio State University. A Fellow of the American StatisticalAssociation and the Institute of Mathematical Statistics, he haspublished extensively in the areas of statistical modeling,analysis of spatial and spatio-temporal data, andempirical-Bayesian and Bayesian methods. He is a recipient of theR.A. Fisher Lectureship, awarded by COPSS to recognize theimportance of statistical methods for scientific investigations.Dr. Cressie is an advisor for the Wiley Series in Probability andStatistics and the author of Statistics for Spatial Data,Revised Edition. Chirstopher K. Wikle, PhD, is Professor of Statistics atthe University of Missouri. Dr. Wikle is a Fellow of the AmericanStatistical Association and the author of more than 100 articles onthe topics of spatio-temporal methodology, spatial statistics,hierarchical models, Bayesian methods, and computational methodsfor large data sets. His work is motivated by problems inclimatology, ecology, fisheries and wildlife, meteorology, andoceanography.


It is a wonderful place to begin studying spatio-temporalprocesses. (Mathematical Reviews Clippings, 1January 2013) Overall, I believe this academic monograph would be anexcellent reference book for researchers and graduate students whoare interested in a systematic and indepth understanding ofstatistical approaches to spatio-temporal data analysis andmodeling. (Journal of the American StatisticalAssociation, 15 March 2013) "Better than any other reference now available, Cressie andWikle bridge the gap between applied science and moderninference. This book is a must for any environmentalscientist or engineer engaged in modeling and computation." - JamesS. Clark, H.L. Blomquist Professor of Environment, DukeUniversity "The future lies at the intersection of a question in science orengineering, a process-based model intended to elucidate thequestion, and the statistical analysis of data to give us an ideaof whether or not the model has done the job. This is what I call'modeling the process, not just the data.' Cressie and Wikle haveprovided a guidebook that will broadly appeal to the scientificcommunity - from statistical neophytes to experts - and which willstand the test of time." - Marc Mangel, Distinguished Professor ofApplied Mathematics and Statistics, University of California SantaCruz "This book, written by two of the world's leading experts onmodeling environmental spatio-temporal processes, is a worthysuccessor to Cressie's earlier classic on spatial statistics.Particularly noteable is its extensive coverage not found in anyother book in statistical science, of hierarchical dynamic processmodeling, a new frontier at the interface between the physical andstatistical sciences. It takes us there with a most-justifiedexcursion into the world of methods such as the extended Kalmanfilter, sequential importance sampling, and INLA, that address thecomputational issues confronted at that frontier. Thiscomprehensive, very readable treatment of hot areas of modernresearch and applications, is written with great clarity andinsight. That and its coverage of a broad range of applications,will make it an essential and long-lived reference for statisticalas well as non-statistical scientists alike." - Jim Zidek,Professor Emeritus and Fellow of the Royal Society of Canada,University of British Columbia "This book is by far the most comprehensive treatment availableon the statistics of spatio-temporal processes and will surelybecome a standard reference in the field. After extensive surveysof time series analysis and traditional spatial statistics, theauthors develop spatio-temporal analysis through a series ofchapters covering empirical and exploratory methods, followed byprobability models for spatio-temporal processes, and then threechapters on the hierarchical dynamical approach which has been atthe core of their own contributions since the late 1990s.Throughout the book, they develop the methods through detaileddescriptions of computational algorithms, leading up to a finalchapter that discusses in-depth applications to predictingsea-surface temperatures and wind speeds, remote-sensing measuresof atmospheric particles, and bird migration. Every researcherinvolved in the analysis of large-scale environmental datasetsshould own a copy of this book." - Richard L. Smith, DistinguishedProfessor of Statistics, University of North Carolina at ChapelHill, and Director, Statistical and Applied Mathematical SciencesInstitute (SAMSI)

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