
Statistical Methods in the Atmospheric Sciences
Resources
Description
Key Features
- Accessible presentation and explanation of techniques for atmospheric data summarization, analysis, testing and forecasting
- Many worked examples
- End-of-chapter exercises, with answers provided
Readership
Table of 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 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 ExercisesChapter 4 Parametric Probability Distributions
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
5.1. Background
5.2 Some Commonly Encountered Parametric Tests
5.3 Nonparametric Tests
5.4 Multiplicity and "Field Significance"
5.5. ExercisesChapter 6 Bayesian Inference
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
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 ExercisesChapter 8 Forecast Verification
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
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 ExercisesIII Multivariate Statistics
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
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 ExercisesChapter 12 Principal Component (EOF) Analysis
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)
13.1 Basics of CCA
13.2 CCA Applied to Fields
13.3 Computational Considerations
13.4 Maximum Covariance Analysis (MCA)
13.5 ExercisesChapter 14 Discrimination and Classification
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
15.1 Background
15.2 Hierarchical Clustering
15.3 Nonhierarchical Clustering
15.4 ExercisesAppendix A Example Data Sets
Appendix B Probability Tables
Appendix C Answers to Exercises
References
Index
Product details
- No. of pages: 704
- Language: English
- Copyright: © Academic Press 2011
- Published: May 20, 2011
- Imprint: Academic Press
- Hardcover ISBN: 9780123850225
- eBook ISBN: 9780123850232
About the Author
Daniel Wilks
Affiliations and Expertise
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