Statistics for Spatio-Temporal Data
1. Edition April 2011
624 Pages, Hardcover
Wiley & Sons Ltd
Short Description
There has been a flurry of relatively recent research activity in spatio-temporal statistics, and this book puts that activity in a perspective that bridges classic concepts with modern hierarchical statistical modeling concepts and the latest computational methods. Since temporal dependence is of a fundamentally different nature that spatial dependence, the dynamical, explanatory aspect of temporal dependence is featured. The authors quantify and exploit spatio-temporal variability in scientific applications, including case studies based on real-world environmental data, with vivid, full-color graphics.
A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods
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.
Acknowledgments.
1 Space-Time: The Next Frontier.
2 Statistical Preliminaries.
2.1 Conditional Probabilities and Hierarchical Modeling (HM).
2.2 Inference and Diagnostics.
2.3 Computation of the Posterior Distribution.
2.4 Graphical Representations of Statistical Dependencies.
2.5 Data/Model/Computing Compromises.
3 Fundamentals of Temporal Processes.
3.1 Characterization of Temporal Processes.
3.2 Introduction to Deterministic Dynamical Systems.
3.3 Time Series Preliminaries.
3.4 Basic Time Series Models.
3.5 Spectral Representation of Temporal Processes.
3.6 Hierarchical Modeling of Time Series.
3.7 Bibliographic Notes.
4 Fundamentals of Spatial Random Processes.
4.1 Geostatistical Processes.
4.2 Lattice Processes.
4.3 Spatial Point Processes.
4.4 Random Sets.
4.5 Bibliographic Notes.
5 Exploratory Methods for Spatio-Temporal Data.
5.1 Visualization.
5.2 Spectral Analysis.
5.3 Empirical Orthogonal Function (EOF) Analysis.
5.4 Extensions of EOF Analysis.
5.5 Principal Oscillation Patterns (POPs).
5.6 Spatio-Temporal Canonical Correlation Analysis (CCA).
5.7 Spatio-Temporal Field Comparisons.
5.8 Bibliographic Notes.
6 Spatio-Temporal Statistical Models.
6.1 Spatio-Temporal Covariance Functions.
6.2 Spatio-Temporal Kriging.
6.3 Stochastic Differential and Difference Equations.
6.4 Time Series of Spatial Processes.
6.5 Spatio-Temporal Point Processes.
6.6 Spatio-Temporal Components-of-Variations Models.
6.7 Bibliographic Notes.
7 Hierarchical Dynamical Spatio-Temporal Models.
7.1 Data Models for the DSTM.
7.2 Process Models for the DSTM: Linear Models.
7.3 Process Models for the DSTM: Nonlinear Models.
7.4 Process Models for the DSTM: Multivariate Models.
7.5 DSTM Parameter Models.
7.6 Dynamical Design of Monitoring Networks.
7.7 Switching the Emphasis of Time and Space.
7.8 Bibliographic Notes.
8 Hierarchical DSTMs: Implementation and Inference.
8.1 DSTM Process: General Implementation and Inference.
8.2 Inference for the DSTM Process: Linear/Gaussian Models.
8.3 Inference for the DSTM Parameters: Linear/Gaussian Models.
8.4 Inference for the DSTM HM: Nonlinear/Non-Gaussian Models.
8.5 Bibliographic Notes.
9 Hierarchical DSTMs: Examples.
9.1 Long-Lead Forecasting of Tropical Pacific Sea Surface Temperatures.
9.2 Remotely Sensed Aerosol Optical Depth.
9.3 Modeling and Forecasting the Eurasian Collared Dove Invasion.
9.4 Mediterranean Surface Vector Winds.
Epilogue.
References.
Index.
Chirstopher K. Wikle, PhD, is Professor of Statistics at the University of Missouri. Dr. Wikle is a Fellow of the American Statistical Association and the author of more than 100 articles on the topics of spatio-temporal methodology, spatial statistics, hierarchical models, Bayesian methods, and computational methods for large data sets. His work is motivated by problems in climatology, ecology, fisheries and wildlife, meteorology, and oceanography.
