Spatiotemporal Data Analysis

✍ Scribed by Gidon Eshel

• Publisher: Princeton University Press
• Year: 2011
• Tongue: English
• Leaves: 336
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
......Page 1
Spatiotemporal Data Analysis......Page 2
Title
......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
Acknowledgments......Page 16
PART 1. FOUNDATIONS......Page 18
ONE Introduction and Motivation......Page 20
TWO Notation and Basic Operations......Page 22
3.1 Vector Spaces......Page 31
3.2 Matrix Rank......Page 37
3.3 Fundamental Spaces Associated with AÎR M×N......Page 42
3.4 Gram-Schmidt Orthogonalization......Page 60
3.5 Summary......Page 64
4.1 Preface......Page 66
4.2 Eigenanalysis Introduced......Page 67
4.3 Eigenanalysis as Spectral Representation......Page 76
4.4 Summary......Page 92
5.1 SVD Introduced......Page 94
5.2 Some Examples......Page 99
5.3 SVD Applications......Page 105
5.4 Summary......Page 109
PART 2. METHODS OF DATA ANALYSIS......Page 112
SIX The Gray World of Practical Data Analysis: An Introduction to Part 2......Page 114
SEVEN Statistics in Deterministic Sciences: An Introduction......Page 115
7.1 Probability Distributions......Page 118
7.2 Degrees of Freedom......Page 123
EIGHT Autocorrelation......Page 128
8.1 Theoretical Autocovariance and Autocorrelation Functions of AR(1) and AR(2)......Page 137
8.2 Acf-Derived Timescale......Page 142
8.3 Summary of Chapters 7 and 8......Page 144
9.2 Setting Up the Problem......Page 145
9.3 The Linear System Ax = b......Page 149
9.4 Least Squares: The SVD View......Page 163
9.5 Some Special Problems Giving Rise to Linear Systems......Page 168
9.6 Statistical Issues in Regression Analysis......Page 184
9.7 Multidimensional Regression and Linear Model Identification......Page 204
9.8 Summary......Page 214
10.2 The Forward Problem......Page 216
10.3 The Inverse Problem......Page 217
11.1 Introduction......Page 219
11.3 Reshaping Multidimensional Data Sets for EOF Analysis......Page 220
11.4 Forming Anomalies and Removing Time Mean......Page 223
11.5 Missing Values, Take 1......Page 224
11.6 Choosing and Interpreting the Covariability Matrix......Page 227
11.7 Calculating the EOFs......Page 237
11.8 Missing Values, Take 2......Page 244
11.9 Projection Time Series, the Principal Components......Page 247
11.10 A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature......Page 253
11.11 Extended EOF Analysis, EEOF......Page 263
11.12 Summary......Page 279
TWELVE. THE SVD ANALYSIS OF TWO FIELDS......Page 280
12.1 A Synthetic Example......Page 284
12.2 A Second Synthetic Example......Page 287
12.3 A Real Data Example......Page 290
12.4 EOFs as a Prefilter to SVD......Page 292
12.5 summary......Page 293
13.1 Homework 1, Corresponding to Chapter 3......Page 295
13.2 Homework 2, Corresponding to Chapter 3......Page 302
13.3 Homework 3, Corresponding to Chapter 3......Page 309
13.4 Homework 4, Corresponding to Chapter 4......Page 311
13.5 Homework 5, Corresponding to Chapter 5......Page 315
13.6 Homework 6, Corresponding to Chapter 8......Page 319
13.7 A Suggested Midterm Exam......Page 322
13.8 A Suggested Final Exam......Page 330
Index......Page 332

✦ Subjects

Финансово-экономические дисциплины;Статистический анализ экономических данных;