Statistics for Spatio-Temporal Data

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thumbnail image: Statistics for Spatio-Temporal Data
Winner of the 2013 DeGroot Prize.

A state-of-the-art presentation of spatio-temporal processes,
bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods

Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.)

From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models.

Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes.

Topics of coverage include:

  • Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs
  • Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes
  • Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation
  • Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data

Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.

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

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