Spatiotemporal Data Analysis

by Eshel, Gidon

• ISBN13: 9780691128917
• ISBN10: 069112891X
• Format: Hardcover
• Copyright: 2011-12-05
• Publisher: Princeton Univ Pr

Summary

A 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.

Author Biography

Gidon Eshel is Bard Center Fellow at Bard College.

Table of Contents

Preface	p. xi
Acknowledgments	p. xv
Foundations
Introduction and Motivation	p. 1
Notation and Basic Operations	p. 3
Matrix Properties, Fundamental Spaces, Orthogonality	p. 12
Vector Spaces	p. 12
Matrix Rank	p. 18
Fundamental Spaces Associated with A	p. 23
Gram-Schmidt Orthogonalization	p. 41
Summary	p. 45
Introduction to Eigenanalysis	p. 47
Preface	p. 47
Eigenanalysis Introduced	p. 48
Eigenanalysis as Spectral Representation	p. 57
Summary	p. 73
The Algebraic Operation of SVD	p. 75
SVD Introduced	p. 75
Some Examples	p. 80
SVD Applications	p. 86
Summary	p. 90
Methods of Data Analysis
The Gray World of Practical Data Analysis: An Introduction to Part 2	p. 95
7	p. 96
Probability Distributions	p. 99
Degrees of Freedom	p. 104
Autocorrelation	p. 109
	p. 118
Acf-derived Timescale	p. 23
Summary of Chapters 7 and 8	p. 125
Regression and Least Squares	p. 126
Prologue	p. 126
Setting Up the Problem	p. 126
The Linear System Ax = b	p. 130
Least Squares: The SVD View	p. 144
Some Special Problems Giving Rise to Linear Systems	p. 149
Statistical Issues in Regression Analysis	p. 165
Multidimensional Regression and Linear Model Identification	p. 185
Summary	p. 195
The fundamental theorem of linear algebra	p. 197
Introduction	p. 197
The Forward Problem	p. 197
The Inverse Problem	p. 198
Empirical orthogonal functions	p. 200
Introduction	p. 200
Data Matrix Structure Convention	p. 201
Reshaping Multidimensional Data Sets for EOF Analysis	p. 201
Forming Anomalies and Removing Time Mean	p. 204
Missing Values, Take 1	p. 205
Choosing and Interpreting the Covariability Matrix	p. 208
Calculating the EOFs	p. 218
Missing Values, Take2	p. 225
Projection Time Series, the Principal Components	p. 228
A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature	p. 234
Extended EOF Analysis, EEOF	p. 244
Summary	p. 260
The svd analysis of two fields	p. 261
A Synthetic Example	p. 265
A Second Synthetic Example	p. 268
A Real Data Example	p. 271
EOFs as a Prefilter to SVD	p. 273
Summary	p. 274
Suggested Homework	p. 276
Corresponding to Chapter 3	p. 276
Corresponding to Chapter 3	p. 283
Corresponding to Chapter 3	p. 290
Corresponding to Chapter 4	p. 292
Corresponding to Chapter 5	p. 296
Corresponding to Chapter 8	p. 300
	p. 303
	p. 311
Index	p. 313
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