Statistics for Spatio-Temporal Data

1 Statistics for Spatio-Temporal DataWILEY SERIES IN PROBABILITY AND STATISTICSE stablished by WALTER A. SHEWHART and SAMUEL S. WILKSE ditors:David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice,Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott,Adrian F. M. Smith, Ruey S. Tsay, Sanford WeisbergEditors Emeriti:Vic Barnett, J. Stuart Hunter, Jozef L. TeugelsA complete list of the titles in this series appears at the end of this for Spatio-Temporal DataNOEL CRESSIED epartment of StatisticsThe Ohio State UniversityCHRISTOPHER K. WIKLED epartment of StatisticsUniversity of MissouriA JOHN WILEY & SONS, INC., PUBLICATIONC opyright 2011 by John Wiley & Sons, Inc. All rights reservedPublished by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system , or transmitted in anyform or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,except as permitted under Section 107 or 108 ofthe 1976 United States Copyright Act, withouteither the prior written permission of the Publisher, or authorization through payment of theappropriate per-copy fee to the Copyright Clearance Center, Inc.

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4 Cm. (Wiley series in probability and Statistics )Includes bibliographical references and 978-0-471-69274-4 (cloth)1. Spatial analysis ( Statistics ) 2. Stochasticprocesses. 3. time -series analysis. I. Wikle,Christopher K., 1963 II. dc222010033576 Printed in Singapore10987654321 Contents in Brief1 Space time : The Next Frontier12 Statistical Preliminaries173 Fundamentals of Temporal Processes554 Fundamentals of Spatial Random Processes1195 Exploratory Methods for Spatio-Temporal Data2436 Spatio-Temporal Statistical Models2977 Hierarchical dynamical Spatio-Temporal Models3618 Hierarchical DSTMs: Implementation and Inference4419 Hierarchical DSTMs: Examples475 Epilogue519 References523 Index571vContentsPrefacexvAcknowledgment sxix1 Space time : The Next Frontier12 Statistical Conditional Probabilities and Hierarchical Modeling (HM), Bayesian Hierarchical Modeling (BHM), Empirical Hierarchical Modeling (EHM), Search for the USS Scorpion, Classical Statistical Modeling, Hierarchical Statistical Modeling, Inference and Diagnostics, Optimal Prediction, Diagnostics, Computation of the Posterior Distribution, Simulation-Based Inference, Markov Chain Monte Carlo (MCMC)

5 , Summaries of the Posterior Distribution, Additional Remarks, Graphical Representations of Statistical Dependencies, Directed and Undirected Graphs, Conditional Independence, Graphical Models for Temporal, Spatial, andSpatio-Temporal Processes, Data/Model/Computing Compromises, 53viiviiiCONTENTS3 Fundamentals of Temporal Characterization of Temporal Processes, Joint and Conditional Distributions, Deterministic and Stochastic Processes, Introduction to Deterministic dynamical Systems, Linear discrete dynamical Systems, Nonlinear discrete dynamical Systems, Bifurcation, Chaos, State-Space Reconstruction, The Need for Statistical Models for DynamicalProcesses, time Series Preliminaries, Basic time Series Models, White-Noise Process, Random-Walk Process, Autoregressive Process, Moving-Average Process, Autoregressive Moving-Average Process, Graphical Models for time Series, Vector Autoregressive Process, Nonlinear time -Series Models, Spectral Representation of Temporal Processes, Spectral Representations via Orthogonal Series, discrete - time Spectral Expansion, Univariate Spectral Analysis, Bivariate Spectral Analysis, Hierarchical Modeling of time Series, Bibliographic Notes, 1164 Fundamentals of Spatial Random Geostatistical Processes, The Variogram and the Covariance Function.

6 Kriging (Optimal Spatial Prediction), Change-of-Support, Spatial Moving Average (SMA) Models, Multivariate Geostatistical Processes, Other Topics, Lattice Processes, Markov-Type Models in Space, The Markov Random Field (MRF), From the Conditional Probabilities to the JointProbability, Some Examples of Auto Spatial Models, The CAR Model, Hierarchical Modeling on a Spatial Lattice: Small AreaEstimation, Simultaneously Specified Spatial Dependence, Other Topics, Spatial Point Processes, The Poisson Point Process and the Cox Process, Spatial Statistical Dependence, Including theKFunction, Distribution Theory for Spatial Point Processes, Disease Mapping from Event Locations, Other Topics, Random Sets, Hit-or-Miss Topology, Hierarchical Models for Objects Based on RandomSets, The Boolean Model, Bibliographic Notes, 2315 Exploratory Methods for Spatio-Temporal Visualization, Animations, Marginal and Conditional Plots, Empirical Covariance/Correlation Functions, Spatio-Temporal LISAs, Spatio-Temporal Parallel Coordinates Plot.

7 Spectral Analysis, Cross-Spectral Analysis, Spatio-Temporal Spectral Analysis, Empirical Orthogonal Function (EOF) Analysis, Spatially Continuous Formulation, Spatially discrete Formulation, Temporal Formulation, Calculation of EOFs, Extensions of EOF Analysis, Complex (Hilbert) EOFs, Multivariate EOF Analysis, Extended EOF Analysis, Principal Oscillation Patterns (POPs), Calculation of POPs, Spatio-Temporal Canonical Correlation Analysis (CCA), Two-Field Spatio-Temporal CCA, time -Lagged CCA, Spatio-Temporal Field Comparisons, Bibliographic Notes, 2926 Spatio-Temporal Statistical Spatio-Temporal Covariance Functions, Theoretical Properties, Stationarity in Space or time , Separability and Full Symmetry, Sums and Products of Covariance Functions, Spatio-Temporal Variogram, Spectral Representation, Taylor s Hypothesis, Spatio-Temporal dynamical Models, Spatio-Temporal Kriging, Simple Kriging, Ordinary Kriging, Optimal Linear Prediction (Kriging)

8 For DynamicalModels, Stochastic Differential and Difference Equations, Spatio-Temporal Statistical Properties, The Diffusion-Injection Equation, Revisited, time Series of Spatial Processes, Continuous Spatial Index (Geostatistical Processes), discrete Spatial Index (Lattice Processes), Spatio-Temporal Point Processes, Spatio-Temporal Components-of-Variation Models, Dimension Reduction in a dynamical Model, Hierarchical Spatio-Temporal Statistical Modeling, Bibliographic Notes, 356 CONTENTSxi7 Hierarchical dynamical Spatio-Temporal Data Models for the DSTM, Linear Mappings with Equal Dimensions, Linear Mappings with Unequal Dimensions, Dimension Reduction, Nonlinear Mappings, Non-Gaussian Data Models, Process Models for the DSTM.

9 Linear Models, Spatio-Temporal Random Walk, Spatial Autoregressive Model, Lagged Nearest-Neighbor Model, PDE-Based Parameterizations, IDE-Based Dynamics, Spectral Parameterizations, Multiresolution DSTMs, Process Models for the DSTM: Nonlinear Models, Local Linear Approximations, State-Dependent Processes, General Quadratic Nonlinearity (GQN), Agent-Based Models, Process Models for the DSTM: Multivariate Models, Augmenting the State Process (Multivariate DSTMs), Dependence on Common Processes, Conditional Formulation, DSTM Parameter Models, Data-Model Parameters, Process-Model Parameters, Deterministic Process Models with RandomParameters, dynamical Design of Monitoring Networks, Switching the Emphasis of time and Space, Bibliographic Notes, 4338 Hierarchical DSTMs: Implementation and DSTM Process: General Implementation and Inference, Sequential Implementation: General, Inference for the DSTM Process: Linear/GaussianModels, Kalman Filter, Kalman Smoother, Inference for the DSTM Parameters.

10 Linear/GaussianModels, EHM Implementation via the EM Algorithm, BHM Implementation via the Gibbs Sampler, Inference for the Hierarchical DSTM: Nonlinear/Non-GaussianModels, Extended Kalman Filter, BHM Implementation via MCMC, Alternative Metropolis Hastings Algorithms andApproximations, Importance Sampling Monte Carlo, Sequential Monte Carlo, Particle Filtering, Ensemble Kalman Filtering, Integrated Nested Laplace Approximation (INLA), Bibliographic Notes, 4729 Hierarchical DSTMs: Long-Lead Forecasting of Tropical Pacific Sea SurfaceTemperatures, Reduced-Dimension Linear DSTM, Reduced-Dimension Nonlinear DSTM, Remotely Sensed Aerosol Optical Depth, AOD Data Model and Process Model, The AOD EHM: Implementation and Inference, Predictions for Aerosol Optical Depth, Modeling and Forecasting the Eurasian Collared Dove Invasion, The Eurasian Collared Dove Invasion of North America, ECD Data Model, ECD Process Model, ECD Parameter Model, The ECD BHM: Implementation and Inference, Mediterranean Surface Vector Winds, Scientific Motivation for the Process Model, The SVW BHM, The SVW BHM.