Spatiotemporal Data Analysis ：Spatiotemporal Data Analysis

Publication subTitle ：Spatiotemporal Data Analysis

Author： Eshel Gidon;;;

Publisher： Princeton University Press‎

Publication year： 2011

E-ISBN: 9781400840632

P-ISBN(Paperback): 9780691128917

Subject： O212.1 General statistics

Keyword：大气科学（气象学）,天文学、地球科学,数学

Language： ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Description

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.

Chapter

Cover

Spatiotemporal Data Analysis

ONE Introduction and Motivation

TWO Notation and Basic Operations

THREE Matrix Properties, Fundamental Spaces, Orthogonality

3.1 Vector Spaces

3.2 Matrix Rank

3.3 Fundamental Spaces Associated with AÎR M×N

3.4 Gram-Schmidt Orthogonalization

3.5 Summary

FOUR Introduction to Eigenanalysis

4.1 Preface

4.2 Eigenanalysis Introduced

4.3 Eigenanalysis as Spectral Representation

4.4 Summary

FIVE The Algebraic Operation of SVD

5.1 SVD Introduced

5.2 Some Examples

5.3 SVD Applications

5.4 Summary

PART 2. METHODS OF DATA ANALYSIS

SIX The Gray World of Practical Data Analysis: An Introduction to Part 2

SEVEN Statistics in Deterministic Sciences: An Introduction

7.1 Probability Distributions

7.2 Degrees of Freedom

EIGHT Autocorrelation

8.1 Theoretical Autocovariance and Autocorrelation Functions of AR(1) and AR(2)

8.2 Acf-Derived Timescale

8.3 Summary of Chapters 7 and 8

NINE Regression and Least Squares

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

Index

The users who browse this book also browse