Spatio-Temporal Statistics With R

✍ Scribed by Christopher Wikle; Andrew Zammit Mangion; Noel Cressie

• Publisher: CRC Press
• Year: 2019
• Tongue: English
• Leaves: 397
• Category: Library

✦ Synopsis

The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more. The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Acknowledgements
Preface
1 Introduction to Spatio-Temporal Statistics
1.1 Why Should Spatio-Temporal Models Be Statistical?
1.2 Goals of Spatio-Temporal Statistics
1.2.1 The Two Ds of Spatio-Temporal Statistical Modeling
1.2.2 Descriptive Modeling
1.2.3 Dynamic Modeling
1.3 Hierarchical Statistical Models
1.4 Structure of the Book
2 Exploring Spatio-Temporal Data
2.1 Spatio-Temporal Data
2.2 Representation of Spatio-Temporal Data in R
2.3 Visualization of Spatio-Temporal Data
2.3.1 Spatial Plots
2.3.2 Time-Series Plots
2.3.3 Hovmöller Plots
2.3.4 Interactive Plots
2.3.5 Animations
2.3.6 Trelliscope: Visualizing Large Spatio-Temporal Data Sets
2.3.7 Visualizing Uncertainty
2.4 Exploratory Analysis of Spatio-Temporal Data
2.4.1 Empirical Spatial Means and Covariances
2.4.2 Spatio-Temporal Covariograms and Semivariograms
2.4.3 Empirical Orthogonal Functions (EOFs)
2.4.4 Spatio-Temporal Canonical Correlation Analysis
2.5 Chapter 2 Wrap-Up
Lab 2.1: Data Wrangling
Lab 2.2: Visualization
Lab 2.3: Exploratory Data Analysis
3 Spatio-Temporal Statistical Models
3.1 Spatio-Temporal Prediction
3.2 Regression (Trend-Surface) Estimation
3.2.1 Model Diagnostics: Dependent Errors
3.2.2 Parameter Inference for Spatio-Temporal Data
3.2.3 Variable Selection
3.3 Spatio-Temporal Forecasting
3.4 Non-Gaussian Errors
3.4.1 Generalized Linear Models and Generalized Additive Models
3.5 Hierarchical Spatio-Temporal Statistical Models
3.6 Chapter 3 Wrap-Up
Lab 3.1: Deterministic Prediction Methods
Lab 3.2: Trend Prediction
Lab 3.3: Regression Models for Forecasting
Lab 3.4: Generalized Linear Spatio-Temporal Regression
4 Descriptive Spatio-Temporal Statistical Models
4.1 Additive Measurement Error and Process Models
4.2 Prediction for Gaussian Data and Processes
4.2.1 Spatio-Temporal Covariance Functions
4.2.2 Spatio-Temporal Semivariograms
4.2.3 Gaussian Spatio-Temporal Model Estimation
4.3 Random-Effects Parameterizations
4.4 Basis-Function Representations
4.4.1 Random Effects with Spatio-Temporal Basis Functions
4.4.2 Random Effects with Spatial Basis Functions
4.4.3 Random Effects with Temporal Basis Functions
4.4.4 Confounding of Fixed Effects and Random Effects
4.5 Non-Gaussian Data Models with Latent Gaussian Processes
4.5.1 Generalized Additive Models (GAMs)
4.5.2 Inference for Spatio-Temporal Hierarchical Models
4.6 Chapter 4 Wrap-Up
Lab 4.1: Spatio-Temporal Kriging with gstat
Lab 4.2: Spatio-Temporal Basis Functions with FRK
Lab 4.3: Temporal Basis Functions with SpatioTemporal
Lab 4.4: Non-Gaussian Spatio-Temporal GAMs with mgcv
Lab 4.5: Non-Gaussian Spatio-Temporal Models with INLA
5 Dynamic Spatio-Temporal Models
5.1 General Dynamic Spatio-Temporal Models
5.1.1 Data Model
5.1.2 Process Model
5.1.3 Parameters
5.2 Latent Linear Gaussian DSTMs
5.2.1 Linear Data Model with Additive Gaussian Error
5.2.2 Non-Gaussian and Nonlinear Data Model
5.2.3 Process Model
5.3 Process and Parameter Dimension Reduction
5.3.1 Parameter Dimension Reduction
5.3.2 Dimension Reduction in the Process Model
5.4 Nonlinear DSTMs
5.5 Chapter 5 Wrap-Up
Lab 5.1: Implementing an IDE Model in One-Dimensional Space
Lab 5.2: Spatio-Temporal Inference using the IDE Model
Lab 5.3: Spatio-Temporal Inference with Unknown Evolution Operator
6 Evaluating Spatio-Temporal Statistical Models
6.1 Comparing Model Output to Data: What Do We Compare?
6.1.1 Comparison to a Simulated “True” Process
6.1.2 Predictive Distributions of the Data
6.1.3 Validation and Cross-Validation
6.2 Model Checking
6.2.1 Extensions of Regression Diagnostics
6.2.2 Graphical Diagnostics
6.2.3 Sensitivity Analysis
6.3 Model Validation
6.3.1 Predictive Model Validation
6.3.2 Spatio-Temporal Validation Statistics
6.3.3 Spatio-Temporal Cross-Validation Measures
6.3.4 Scoring Rules
6.3.5 Field Comparison
6.4 Model Selection
6.4.1 Model Averaging
6.4.2 Model Comparison via Bayes Factors
6.4.3 Model Comparison via Validation
6.4.4 Information Criteria
6.5 Chapter 6 Wrap-Up
Lab 6.1: Spatio-Temporal Model Validation
Pergimus (Epilogue)
Appendices
A: Some Useful Matrix-Algebra Definitions and Properties
B: General Smoothing Kernels
C: Estimation and Prediction for Dynamic Spatio-Temporal Models
C.1 Estimation in Vector Autoregressive Spatio-Temporal Models via the Method of Moments
C.2 Prediction and Estimation in Fully Parameterized Linear DSTMs
C.3 Estimation for Non-Gaussian and Nonlinear DSTMs
D: Mechanistically Motivated Dynamic Spatio-Temporal Models
D.1 Example of a Process Model Motivated by a PDE: Finite Differences
D.2 Example of a Process Model Motivated by a PDE: Spectral
D.3 Example of a Process Model Motivated by an IDE
E: Case Study: Physical-Statistical Bayesian Hierarchical Model for Predicting Mediterranean Surface Winds
F: Case Study: Quadratic Echo State Networks for Sea Surface Temperature Long-Lead Prediction
List of R Packages
References
Subject Index
Author Index
R Function Index