Eshel G. Spatiotemporal Data Analysis

Princeton University Press – 2012, 338 pages
ISBN: 069112891XA severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics-origin, rates, and frequencies-of these phenomena. This comprehensive text introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine.Gidon Eshel begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. He then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams.Part I. Foundations
Chapter One: Introduction and Motivation
Chapter Two: Notation and Basic Operations
Chapter Three: Matrix Properties, Fundamental Spaces, Orthogonality
Vector Spaces
Matrix Rank
Fundamental Spaces Associated with A d R M # N
Gram-Schmidt OrthogonalizationChapter Four: Introduction to EigenanalysisEigenanalysis Introduced
Eigenanalysis as Spectral RepresentationChapter Five: The Algebraic Operation of SVD
SVD Introduced
Some Examples
SVD ApplicationsPart II. Methods of Data Analysis
Chapter Six: The Gray World of Practical Data Analysis: An Introduction to Part
Chapter Seven Statistics in Deterministic Sciences: An Introduction
. Probability Distributions
. Degrees of Freedom
Chapter Eight: Autocorrelation
. Theoretical Autocovariance and Autocorrelation Functions of AR() and AR()
. Acf-derived Timescale
. Summary of Chapters and
Chapter Nine: Regression and Least Squares
. Prologue
. Setting Up the Problem
. The Linear System Ax = b
. Least Squares: The SVD View
. Some Special Problems Giving Rise to Linear Systems
. Statistical Issues in Regression Analysis
. Multidimensional Regression and Linear Model Identification
. Summary
Chapter Ten:. The Fundamental Theorem of Linear Algebra
. Introduction
. The Forward Problem
. The Inverse Problem
Chapter Eleven:. Empirical Orthogonal FunctionsData Matrix Structure Convention
Reshaping Multidimensional Data Sets for EOF Analysis
Forming Anomalies and Removing Time Mean
Missing Values, Take
Choosing and Interpreting the Covariability Matrix
Calculating the EOFs
Missing Values, Take
Projection Time Series, the Principal Components
A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature
Extended EOF Analysis, EEOFChapter Twelve:. The SVD Analysis of Two Fields
A Synthetic Example
A Second Synthetic Example
A Real Data Example
EOFs as a Prefilter to SVDChapter Thirteen:. Suggested Homework
Homework 1, Corresponding to Chapter 3
Homework 2, Corresponding to Chapter 3
Homework 3, Corresponding to Chapter 3
Homework 4, Corresponding to Chapter 4
Homework 5, Corresponding to Chapter 5
Homework 6, Corresponding to Chapter 8
A Suggested Midterm Exam
A Suggested Final Exam