Spatiotemporal Data Analysis

Gidon Eshel

• Publisher: Princeton University Press
• Year: 2011
• Print ISBN: 9780691128917
• eBook ISBN: 9781400840632
• Topic: Naturwissenschaften
• Subtopic: Lineare Algebra

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.

PART 1

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Foundations

ONE

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Introduction and Motivation

BEFORE YOU START working your way through this book, you may ask yourself—Why analyze data? This is an important, basic question, and it has several compelling answers.

The simplest need for data analysis arises most naturally in disciplines addressing phenomena that are, in all likelihood, inherently nondeterministic (e.g., feelings and psychology or stock market behavior). Since such fields of knowledge are not governed by known fundamental equations, the only way to generalize disparate observations into expanded knowledge is to analyze those observations. In addition, in such fields predictions are entirely dependent on empirical models of the types discussed in chapter 9 that contain parameters not fundamentally constrained by theory. Finding these models’ numerical values most suitable for a particular application is another important role of data analysis.

A more general rationale for analyzing data stems from the complementary relationship of empirical and theoretical science and dominates contexts and disciplines in which the studied phenomena have, at least in principle, fully knowable and usable fundamental governing dynamics (see chapter 7). In these contexts, best exemplified by physics, theory and observations both vie for the helm. Indeed, throughout the history of physics, theoretical predictions of yet unobserved phenomena and empirical observations of yet theoretically unexplained ones have alternately fixed physics’ ropes.¹ When theory leads, its predictions must be tested against experimental or observational data. When empiricism is at the helm, coherent, reproducible knowledge is systematically and carefully gleaned from noisy, messy observations. At the core of both, of course, is data analysis.

Empiricism’s biggest triumph, affording it (ever so fleetingly) the leadership role, arises when novel data analysis-based knowledge—fully acqu...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• Part 1 Foundations
• Part 2 Methods of Data Analysis
• Index