Statistical Methods in the Atmospheric Sciences

I Preliminaries
Chapter 1 Introduction
 1.1 What Is Statistics?
 1.2 Descriptive and Inferential Statistics
 1.3 Uncertainty about the Atmosphere

Chapter 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 Exercises

II 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 Exercises

Chapter 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 Exercises

Chapter 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. Exercises

Chapter 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 Exercises

Chapter 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 Exercises

Chapter 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 Exercises

Chapter 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 Exercises

III 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 Exercises

Chapter 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 Exercises

Chapter 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 Exercises

Chapter 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 Exercises

Chapter 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 Exercises

Chapter 15 Cluster Analysis
 15.1 Background 
 15.2 Hierarchical Clustering
 15.3 Nonhierarchical Clustering
 15.4 Exercises

Appendix A  Example Data Sets
Appendix B Probability Tables
Appendix C Answers to Exercises
References
Index