Spatiotemporal data analysis

Description

For statistics to be used by sociologists, and especially by students of sociology, they must first be easy to understand and use. Accordingly this book is aimed at that legion of professional sociologists and students who have always feared numbers; it employs much visual display, for example, as an easy way into the data. Also, the book is written in a relaxed and enthusiastic way that reassures apprehensive students without watering down what they must be taught. Classical statistics were developed to meet the requirements of the natural sciences; as such they reflect the more deductive nature of hypothesis development in these sciences. However, they have offered the sociologists little in the way of techniques for exploring messy data in the context of incomplete theories. This book attempts to remedy those weaknesses, and it emphasizes exploratory data techniques which sociologists will find useful in their day-to-day research. The primary characteristics of exploratory techniques discussed by the authors are simplicity, resistance and elucidation. Its coverage is from basic statistics up to multiple regression and two-way anova. The inter-relationship between exploratory and confirmatory techniques is stressed, and, through the alternating presentation of each, the students learn to master data analysis: to be and to feel in control "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"--  Read more... 9.1.Prologue -- 9.2.Setting Up the Problem -- 9.3.The Linear System Ax = b -- 9.4.Least Squares: The SVD View -- 9.5.Some Special Problems Giving Rise to Linear Systems -- 9.6.Statistical Issues in Regression Analysis -- 9.7.Multidimensional Regression and Linear Model Identification -- 9.8.Summary -- Ten.The Fundamental Theorem Of Linear Algebra -- 10.1.Introduction -- 10.2.The Forward Problem -- 10.3.The Inverse Problem -- Eleven.Empirical Orthogonal Functions -- 11.1.Introduction -- 11.2.Data Matrix Structure Convention -- 11.3.Reshaping Multidimensional Data Sets for EOF Analysis -- 11.4.Forming Anomalies and Removing Time Mean -- 11.5.Missing Values, Take 1 -- 11.6.Choosing and Interpreting the Covariability Matrix -- 11.7.Calculating the EOFs -- 11.8.Missing Values, Take 2 -- 11.9.Projection Time Series, the Principal Components -- 11.10.A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature -- 11.11.Extended EOF Analysis, EEOF 11.12.Summary -- Twelve.The Svd Analysis Of Two Fields -- 12.1.A Synthetic Example -- 12.2.A Second Synthetic Example -- 12.3.A Real Data Example -- 12.4.EOFs as a Prefilter to SVD -- 12.5.Summary -- Thirteen.Suggested Homework -- 13.1.Homework 1, Corresponding to Chapter 3 -- 13.2.Homework 2, Corresponding to Chapter 3 -- 13.3.Homework 3, Corresponding to Chapter 3 -- 13.4.Homework 4, Corresponding to Chapter 4 -- 13.5.Homework 5, Corresponding to Chapter 5 -- 13.6.Homework 6, Corresponding to Chapter 8 -- 13.7.A Suggested Midterm Exam -- 13.8.A Suggested Final Exam