Statistics for Spatio-Temporal Data

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