Statistical Methods in the Atmospheric Sciences
By- Daniel Wilks, Cornell University, Ithaca, New York, U.S.A.
Praise for the First Edition:"I recommend this book, without hesitation, as either a reference or course text...Wilks' excellent book provides a thorough base in applied statistical methods for atmospheric sciences."--BAMS (Bulletin of the American Meteorological Society)Fundamentally, statistics is concerned with managing data and making inferences and forecasts in the face of uncertainty. It should not be surprising, therefore, that statistical methods have a key role to play in the atmospheric sciences. It is the uncertainty in atmospheric behavior that continues to move research forward and drive innovations in atmospheric modeling and prediction.This revised and expanded text explains the latest statistical methods that are being used to describe, analyze, test and forecast atmospheric data. It features numerous worked examples, illustrations, equations, and exercises with separate solutions. Statistical Methods in the Atmospheric Sciences, Second Edition will help advanced students and professionals understand and communicate what their data sets have to say, and make sense of the scientific literature in meteorology, climatology, and related disciplines.
Audience
Researchers and students in the atmospheric sciences, including meteorology, climatology, and other geophysical disciplines
International Geophysics
Hardbound, 704 Pages
Published: May 2011
Imprint: Academic Press
ISBN: 978-0-12-385022-5
Reviews
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"I would strongly recommend this book... To those who already posses the first edition and are satisfied users, you would be hard-pressed to do without the second edition."--Bulletin of the American Meteorological Society "What makes this book specific to meterology, and not just to applied statistics, are it's extensive examples and two chapters on statistcal forecasting and forecast evaluation."--William (Matt) Briggs, Weill Medical College of Cornell University "Wilks (earth and atmospheric sciences, Cornell U.) presents a textbook for an upper-division undergraduate or beginning graduate course for students who have completed a first course in statistics and are interested in learning further statistics in the context of atmospheric sciences. No mathematics beyond first-year calculus is required, nor any background in atmospheric science, though some would be helpful. He also has in mind researchers using the book as a reference. No dates are cited for previous editions, this one adds a chapter on Bayesian inference, updates the treatment throughout, and includes new references to recently published literature."--SciTech Book News
Contents
I Preliminaries
Chapter 1 Introduction
1.1 What Is Statistics?
1.2 Descriptive and Inferential Statistics
1.3 Uncertainty about the AtmosphereChapter 2 Review of Probability
2.1 Background
2.2 The Elements of Probability
2.3 The Meaning of Probability
2.4 Some Properties of Probability
2.5 ExercisesII Univariate Statistics
Chapter 4 Parametric Probability Distributions
Chapter 3 Empirical Distributions and Exploratory Data Analysis
3.1 Background
3.2 Numerical Summary Measures
3.3 Graphical Summary Devices
3.4 Reexpression
3.5 Exploratory Techniques for Paired Data
3.6 Exploratory Techniques for Higher-Dimensional Data
3.7 Exercises
4.1 Background
4.2 Discrete Distributions
4.3 Statistical Expectations
4.4 Continuous Distributions
4.5 Qualitative Assessments of the Goodness of Fit
4.6 Parameter Fitting Using Maximum Likelihood
4.7 Statistical Simulation
4.8 ExercisesChapter 5 Frequentist Statistical Inference
Chapter 6 Bayesian Inference
5.1. Background
5.2 Some Commonly Encountered Parametric Tests
5.3 Nonparametric Tests
5.4 Multiplicity and "Field Significance"
5.5. Exercises
6.1 Background
6.2 The Structure of Bayesian Inference
6.3 Conjugate Distributions
6.4 Dealing With Difficult Integrals
6.5 ExercisesChapter 7 Statistical Forecasting
Chapter 8 Forecast Verification
7.1 Background
7.2 Linear Regression
7.3 Nonlinear Regression
7.4 Predictor Selection
7.5 Objective Forecasts Using Traditional Statistical Methods
7.6 Ensemble Forecasting
7.7 Ensemble MOS
7.8 Subjective Probability Forecasts
7.9 Exercises
8.1 Background
8.2 Nonprobabilistic Forecasts for Discrete Predictands
8.3 Nonprobabilistic Forecasts for Continuous Predictands
8.4 Probability Forecasts for Discrete Predictands
8.5 Probability Forecasts for Continuous Predictands
8.6 Nonprobabilistic Forecasts for Fields
8.7 Verification of Ensemble Forecasts
8.8 Verification Based on Economic Value
8.9 Verification When the Observation is Uncertain
8.10 Sampling and Inference for Verification Statistics
8.11 ExercisesChapter 9 Time Series
III Multivariate Statistics
9.1 Background
9.2 Time Domain-I. Discrete Data
9.3 Time Domain-II. Continuous Data
9.4 Frequency Domain-I. Harmonic Analysis
9.5 Frequency Domain-II. Spectral Analysis
9.6 Exercises
Chapter 10 Matrix Algebra and Random Matrices
10.1 Background to Multivariate Statistics
10.2 Multivariate Distance
10.3 Matrix Algebra Review
10.4 Random Vectors and Matrices
10.5 ExercisesChapter 11 The Multivariate Normal (MVN) Distribution
Chapter 12 Principal Component (EOF) Analysis
11.1 Definition of the MVN
11.2 Four Handy Properties of the MVN
11.3 Assessing Multinormality
11.4 Simulation from the Multivariate Normal Distribution
11.5 Inferences about a Multinormal Mean Vector
11.6 Exercises
12.1 Basics of Principal Component Analysis
12.2 Application of PCA to Geophysical Fields
12.3 Truncation of the Principal Components
12.4 Sampling Properties of the Eigenvalues and Eigenvectors
12.5 Rotation of the Eigenvectors
12.6 Computational Considerations
12.7 Some Additional Uses of PCA
12.8 ExercisesChapter 13 Canonical Correlation Analysis (CCA)
Chapter 14 Discrimination and Classification
13.1 Basics of CCA
13.2 CCA Applied to Fields
13.3 Computational Considerations
13.4 Maximum Covariance Analysis (MCA)
13.5 Exercises
14.1 Discrimination vs. Classification
14.2 Separating Two Populations
14.3 Multiple Discriminant Analysis (MDA)
14.4 Forecasting with Discriminant Analysis
14.5 Alternatives to Classical Discriminant Analysis
14.6 ExercisesChapter 15 Cluster Analysis
Appendix A Example Data Sets
15.1 Background
15.2 Hierarchical Clustering
15.3 Nonhierarchical Clustering
15.4 Exercises
Appendix B Probability Tables
Appendix C Answers to Exercises
References
Index
