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E-grāmata: Statistical Methods in the Atmospheric Sciences

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(Department of Earth and Atmospheric Sciences, Cornell University, USA)
  • Formāts: PDF+DRM
  • Sērija : International Geophysics
  • Izdošanas datums: 04-Jul-2011
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780123850232
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Statistical Methods in the Atmospheric SciencesPalielināt
  • Formāts: PDF+DRM
  • Sērija : International Geophysics
  • Izdošanas datums: 04-Jul-2011
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780123850232
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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. Academic Press in an imprint of Elsevier. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

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.

  • Accessible presentation and explanation of techniques for atmospheric data summarization, analysis, testing and forecasting

  • Many worked examples

  • End-of-chapter exercises, with answers provided

    • Recenzijas

    "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

    Papildus informācija

    Expanded coverage and key updates help readers describe, analyze, test, and forecast atmospheric data.
    Preface v
    Part I Preliminaries
    		1(20)
    1 Introduction
    		3(4)
    1.1 What Is Statistics?
    		3(1)
    1.2 Descriptive and Inferential Statistics
    		3(1)
    1.3 Uncertainty about the Atmosphere
    		4(3)
    2 Review of Probability
    		7(14)
    2.1 Background
    		7(1)
    2.2 The Elements of Probability
    		7(2)
    2.2.1 Events
    		7(1)
    2.2.2 The Sample Space
    		8(1)
    2.2.3 The Axioms of Probability
    		9(1)
    2.3 The Meaning of Probability
    		9(1)
    2.3.1 Frequency Interpretation
    		9(1)
    2.3.2 Bayesian (Subjective) Interpretation
    		10(1)
    2.4 Some Properties of Probability
    		10(8)
    2.4.1 Domain, Subsets, Complements, and Unions
    		11(1)
    2.4.2 DeMorgan's Laws
    		12(1)
    2.4.3 Conditional Probability
    		13(1)
    2.4.4 Independence
    		14(2)
    2.4.5 Law of Total Probability
    		16(1)
    2.4.6 Bayes' Theorem
    		17(1)
    2.5 Exercises
    		18(3)
    Part II Univariate Statistics
    		21(436)
    3 Empirical Distributions and Exploratory Data Analysis
    		23(48)
    3.1 Background
    		23(2)
    3.1.1 Robustness and Resistance
    		23(1)
    3.1.2 Quantiles
    		24(1)
    3.2 Numerical Summary Measures
    		25(3)
    3.2.1 Location
    		26(1)
    3.2.2 Spread
    		26(1)
    3.2.3 Symmetry
    		27(1)
    3.3 Graphical Summary Devices
    		28(14)
    3.3.1 Stem-and-Leaf Display
    		28(1)
    3.3.2 Boxplots
    		29(2)
    3.3.3 Schematic Plots
    		31(2)
    3.3.4 Other Boxplot Variants
    		33(1)
    3.3.5 Histograms
    		33(1)
    3.3.6 Kernel Density Smoothing
    		34(5)
    3.3.7 Cumulative Frequency Distributions
    		39(3)
    3.4 Reexpression
    		42(7)
    3.4.1 Power Transformations
    		42(4)
    3.4.2 Standardized Anomalies
    		46(3)
    3.5 Exploratory Techniques for Paired Data
    		49(11)
    3.5.1 Scatterplots
    		50(1)
    3.5.2 Pearson (Ordinary) Correlation
    		50(5)
    3.5.3 Spearman Rank Correlation and Kendall's τ
    		55(2)
    3.5.4 Serial Correlation
    		57(2)
    3.5.5 Autocorrelation Function
    		59(1)
    3.6 Exploratory Techniques for Higher-Dimensional Data
    		60(10)
    3.6.1 The Star Plot
    		60(1)
    3.6.2 The Glyph Scatterplot
    		61(2)
    3.6.3 The Rotating Scatterplot
    		63(1)
    3.6.4 The Correlation Matrix
    		63(3)
    3.6.5 The Scatterplot Matrix
    		66(1)
    3.6.6 Correlation Maps
    		67(3)
    3.7 Exercises
    		70(1)
    4 Parametric Probability Distributions
    		71(62)
    4.1 Background
    		71(2)
    4.1.1 Parametric versus Empirical Distributions
    		71(1)
    4.1.2 What Is a Parametric Distribution?
    		72(1)
    4.1.3 Parameters versus Statistics
    		72(1)
    4.1.4 Discrete versus Continuous Distributions
    		72(1)
    4.2 Discrete Distributions
    		73(9)
    4.2.1 Binomial Distribution
    		73(3)
    4.2.2 Geometric Distribution
    		76(1)
    4.2.3 Negative Binomial Distribution
    		77(3)
    4.2.4 Poisson Distribution
    		80(2)
    4.3 Statistical Expectations
    		82(3)
    4.3.1 Expected Value of a Random Variable
    		82(1)
    4.3.2 Expected Value of a Function of a Random Variable
    		83(2)
    4.4 Continuous Distributions
    		85(27)
    4.4.1 Distribution Functions and Expected Values
    		85(2)
    4.4.2 Gaussian Distributions
    		87(8)
    4.4.3 Gamma Distributions
    		95(8)
    4.4.4 Beta Distributions
    		103(2)
    4.4.5 Extreme-Value Distributions
    		105(5)
    4.4.6 Mixture Distributions
    		110(2)
    4.5 Qualitative Assessments of the Goodness of Fit
    		112(4)
    4.5.1 Superposition of a Fitted Parametric Distribution and Data Histogram
    		113(2)
    4.5.2 Quantile---Quantile (Q---Q) Plots
    		115(1)
    4.6 Parameter Fitting Using Maximum Likelihood
    		116(6)
    4.6.1 The Likelihood Function
    		116(2)
    4.6.2 The Newton-Raphson Method
    		118(1)
    4.6.3 The EM Algorithm
    		119(3)
    4.6.4 Sampling Distribution of Maximum-Likelihood Estimates
    		122(1)
    4.7 Statistical Simulation
    		122(8)
    4.7.1 Uniform Random-Number Generators
    		123(2)
    4.7.2 Nonuniform Random-Number Generation by Inversion
    		125(1)
    4.7.3 Nonuniform Random-Number Generation by Rejection
    		126(2)
    4.7.4 Box-Muller Method for Gaussian Random-Number Generation
    		128(1)
    4.7.5 Simulating from Mixture Distributions and Kernel Density Estimates
    		128(2)
    4.8 Exercises
    		130(3)
    5 Frequentist Statistical Inference
    		133(54)
    5.1 Background
    		133(8)
    5.1.1 Parametric versus Nonparametric Inference
    		133(1)
    5.1.2 The Sampling Distribution
    		134(1)
    5.1.3 The Elements of Any Hypothesis Test
    		134(1)
    5.1.4 Test Levels and p Values
    		135(1)
    5.1.5 Error Types and the Power of a Test
    		135(1)
    5.1.6 One-Sided versus Two-Sided Tests
    		136(1)
    5.1.7 Confidence Intervals: Inverting Hypothesis Tests
    		137(4)
    5.2 Some Commonly Encountered Parametric Tests
    		141(17)
    5.2.1 One-Sample t Test
    		141(1)
    5.2.2 Tests for Differences of Mean under Independence
    		142(2)
    5.2.3 Tests for Differences of Mean for Paired Samples
    		144(1)
    5.2.4 Tests for Differences of Mean under Serial Dependence
    		145(4)
    5.2.5 Goodness-of-Fit Tests
    		149(7)
    5.2.6 Likelihood Ratio Tests
    		156(2)
    5.3 Nonparametric Tests
    		158(20)
    5.3.1 Classical Nonparametric Tests for Location
    		159(7)
    5.3.2 Mann-Kendall Trend Test
    		166(2)
    5.3.3 Introduction to Resampling Tests
    		168(1)
    5.3.4 Permutation Tests
    		169(3)
    5.3.5 The Bootstrap
    		172(6)
    5.4 Multiplicity and "Field Significance"
    		178(7)
    5.4.1 The Multiplicity Problem for Independent Tests
    		178(2)
    5.4.2 Field Significance and the False Discovery Rate
    		180(1)
    5.4.3 Field Significance and Spatial Correlation
    		181(4)
    5.5 Exercises
    		185(2)
    6 Bayesian Inference
    		187(28)
    6.1 Background
    		187(1)
    6.2 The Structure of Bayesian Inference
    		188(6)
    6.2.1 Bayes' Theorem for Continuous Variables
    		188(3)
    6.2.2 Inference and the Posterior Distribution
    		191(1)
    6.2.3 The Role of the Prior Distribution
    		192(2)
    6.2.4 The Predictive Distribution
    		194(1)
    6.3 Conjugate Distributions
    		194(12)
    6.3.1 Definition of Conjugate Distributions
    		194(1)
    6.3.2 Binomial Data-Generating Process
    		195(4)
    6.3.3 Poisson Data-Generating Process
    		199(4)
    6.3.4 Gaussian Data-Generating Process
    		203(3)
    6.4 Dealing with Difficult Integrals
    		206(7)
    6.4.1 Markov Chain Monte Carlo (MCMC) Methods
    		206(1)
    6.4.2 The Metropolis-Hastings Algorithm
    		207(3)
    6.4.3 The Gibbs Sampler
    		210(3)
    6.5 Exercises
    		213(2)
    7 Statistical Forecasting
    		215(86)
    7.1 Background
    		215(1)
    7.2 Linear Regression
    		215(22)
    7.2.1 Simple Linear Regression
    		216(2)
    7.2.2 Distribution of the Residuals
    		218(2)
    7.2.3 The Analysis of Variance Table
    		220(1)
    7.2.4 Goodness-of-Fit Measures
    		221(2)
    7.2.5 Sampling Distributions of the Regression Coefficients
    		223(2)
    7.2.6 Examining Residuals
    		225(5)
    7.2.7 Prediction Intervals
    		230(3)
    7.2.8 Multiple Linear Regression
    		233(1)
    7.2.9 Derived Predictor Variables in Multiple Regression
    		233(4)
    7.3 Nonlinear Regression
    		237(7)
    7.3.1 Generalized Linear Models
    		237(1)
    7.3.2 Logistic Regression
    		238(4)
    7.3.3 Poisson Regression
    		242(2)
    7.4 Predictor Selection
    		244(11)
    7.4.1 Why Is Careful Predictor Selection Important?
    		244(3)
    7.4.2 Screening Predictors
    		247(2)
    7.4.3 Stopping Rules
    		249(3)
    7.4.4 Cross Validation
    		252(3)
    7.5 Objective Forecasts Using Traditional Statistical Methods
    		255(12)
    7.5.1 Classical Statistical Forecasting
    		255(2)
    7.5.2 Perfect Prog and MOS
    		257(7)
    7.5.3 Operational MOS Forecasts
    		264(3)
    7.6 Ensemble Forecasting
    		267(17)
    7.6.1 Probabilistic Field Forecasts
    		267(1)
    7.6.2 Stochastic Dynamical Systems in Phase Space
    		267(3)
    7.6.3 Ensemble Forecasts
    		270(1)
    7.6.4 Choosing Initial Ensemble Members
    		271(2)
    7.6.5 Ensemble Average and Ensemble Dispersion
    		273(2)
    7.6.6 Graphical Display of Ensemble Forecast Information
    		275(7)
    7.6.7 Effects of Model Errors
    		282(2)
    7.7 Ensemble MOS
    		284(8)
    7.7.1 Why Ensembles Need Postprocessing
    		284(2)
    7.7.2 Regression Methods
    		286(4)
    7.7.3 Kernel Density (Ensemble "Dressing") Methods
    		290(2)
    7.8 Subjective Probability Forecasts
    		292(6)
    7.8.1 The Nature of Subjective Forecasts
    		292(1)
    7.8.2 The Subjective Distribution
    		293(1)
    7.8.3 Central Credible Interval Forecasts
    		294(2)
    7.8.4 Assessing Discrete Probabilities
    		296(1)
    7.8.5 Assessing Continuous Distributions
    		297(1)
    7.9 Exercises
    		298(3)
    8 Forecast Verification
    		301(94)
    8.1 Background
    		301(5)
    8.1.1 Purposes of Forecast Verification
    		301(1)
    8.1.2 The Joint Distribution of Forecasts and Observations
    		302(1)
    8.1.3 Scalar Attributes of Forecast Performance
    		303(2)
    8.1.4 Forecast Skill
    		305(1)
    8.2 Nonprobabilistic Forecasts for Discrete Predictands
    		306(17)
    8.2.1 The 2 x 2 Contingency Table
    		306(2)
    8.2.2 Scalar Attributes of the 2 x 2 Contingency Table
    		308(3)
    8.2.3 Skill Scores for 2 x 2 Contingency Tables
    		311(4)
    8.2.4 Which Score?
    		315(1)
    8.2.5 Conversion of Probabilistic to Nonprobabilistic Forecasts
    		316(2)
    8.2.6 Extensions for Multicategory Discrete Predictands
    		318(5)
    8.3 Nonprobabilistic Forecasts for Continuous Predictands
    		323(6)
    8.3.1 Conditional Quantile Plots
    		324(1)
    8.3.2 Scalar Accuracy Measures
    		325(2)
    8.3.3 Skill Scores
    		327(2)
    8.4 Probability Forecasts for Discrete Predictands
    		329(22)
    8.4.1 The Joint Distribution for Dichotomous Events
    		329(2)
    8.4.2 The Brier Score
    		331(1)
    8.4.3 Algebraic Decomposition of the Brier Score
    		332(2)
    8.4.4 The Reliability Diagram
    		334(6)
    8.4.5 The Discrimination Diagram
    		340(1)
    8.4.6 The Logarithmic, or Ignorance Score
    		341(1)
    8.4.7 The ROC Diagram
    		342(4)
    8.4.8 Hedging, and Strictly Proper Scoring Rules
    		346(2)
    8.4.9 Probability Forecasts for Multiple-Category Events
    		348(3)
    8.5 Probability Forecasts for Continuous Predictands
    		351(4)
    8.5.1 Full Continuous Forecast Probability Distributions
    		351(3)
    8.5.2 Central Credible Interval Forecasts
    		354(1)
    8.6 Nonprobabilistic Forecasts for Fields
    		355(14)
    8.6.1 General Considerations for Field Forecasts
    		355(2)
    8.6.2 The S1 Score
    		357(2)
    8.6.3 Mean Squared Error
    		359(5)
    8.6.4 Anomaly Correlation
    		364(3)
    8.6.5 Field Verification Based on Spatial Structure
    		367(2)
    8.7 Verification of Ensemble Forecasts
    		369(8)
    8.7.1 Characteristics of a Good Ensemble Forecast
    		369(2)
    8.7.2 The Verification Rank Histogram
    		371(4)
    8.7.3 Minimum Spanning Tree (MST) Histogram
    		375(1)
    8.7.4 Shadowing, and Bounding Boxes
    		376(1)
    8.8 Verification Based on Economic Value
    		377(5)
    8.8.1 Optimal Decision Making and the Cost/Loss Ratio Problem
    		377(2)
    8.8.2 The Value Score
    		379(2)
    8.8.3 Connections with Other Verification Approaches
    		381(1)
    8.9 Verification When the Observation is Uncertain
    		382(1)
    8.10 Sampling and Inference for Verification Statistics
    		383(8)
    8.10.1 Sampling Characteristics of Contingency Table Statistics
    		383(3)
    8.10.2 ROC Diagram Sampling Characteristics
    		386(2)
    8.10.3 Brier Score and Brier Skill Score Inference
    		388(1)
    8.10.4 Reliability Diagram Sampling Characteristics
    		389(1)
    8.10.5 Resampling Verification Statistics
    		390(1)
    8.11 Exercises
    		391(4)
    9 Time Series
    		395(62)
    9.1 Background
    		395(2)
    9.1.1 Stationary
    		395(1)
    9.1.2 Time-Series Models
    		396(1)
    9.1.3 Time-Domain versus Frequency-Domain Approaches
    		396(1)
    9.2. Time Domain---I Discrete Data
    		397(13)
    9.2.1 Markov Chains
    		397(1)
    9.2.2 Two-State, First-Order Markov Chains
    		398(4)
    9.2.3 Test for Independence versus First-Order Serial Dependence
    		402(2)
    9.2.4 Some Applications of Two-State Markov Chains
    		404(2)
    9.2.5 Multiple-State Markov Chains
    		406(1)
    9.2.6 Higher-Order Markov Chains
    		407(1)
    9.2.7 Deciding among Alternative Orders of Markov Chains
    		408(2)
    9.3. Time Domain---II Continuous Data
    		410(18)
    9.3.1 First-Order Autoregression
    		410(4)
    9.3.2 Higher-Order Autoregressions
    		414(1)
    9.3.3 The AR(2) Model
    		415(4)
    9.3.4 Order Selection Criteria
    		419(2)
    9.3.5 The Variance of a Time Average
    		421(2)
    9.3.6 Autoregressive-Moving Average Models
    		423(1)
    9.3.7 Simulation and Forecasting with Continuous Time-Domain Models
    		424(4)
    9.4. Frequency Domain---I Harmonic Analysis
    		428(10)
    9.4.1 Cosine and Sine Functions
    		428(1)
    9.4.2 Representing a Simple Time Series with a Harmonic Function
    		429(3)
    9.4.3 Estimation of the Amplitude and Phase of a Single Harmonic
    		432(3)
    9.4.4 Higher Harmonics
    		435(3)
    9.5 Frequency Domain---II Spectral Analysis
    		438(17)
    9.5.1 The Harmonic Functions as Uncorrelated Regression Predictors
    		438(2)
    9.5.2 The Periodogram, or Fourier Line Spectrum
    		440(4)
    9.5.3 Computing Spectra
    		444(1)
    9.5.4 Aliasing
    		445(2)
    9.5.5 The Spectra of Autoregressive Models
    		447(3)
    9.5.6 Sampling Properties of Spectral Estimates
    		450(5)
    9.6 Exercises
    		455(2)
    Part III Multivariate Statistics
    		457(160)
    10 Matrix Algebra and Random Matrices
    		459(32)
    10.1 Background to Multivariate Statistics
    		459(2)
    10.1.1 Contrasts between Multivariate and Univariate Statistics
    		459(1)
    10.1.2 Organization of Data and Basic Notation
    		459(1)
    10.1.3 Multivariate Extensions of Common Univariate Statistics
    		460(1)
    10.2 Multivariate Distance
    		461(3)
    10.2.1 Euclidean Distance
    		462(1)
    10.2.2 Mahalanobis (Statistical) Distance
    		463(1)
    10.3 Matrix Algebra Review
    		464(18)
    10.3.1 Vectors
    		464(3)
    10.3.2 Matrices
    		467(9)
    10.3.3 Eigenvalues and Eigenvectors of a Square Matrix
    		476(3)
    10.3.4 Square Roots of a Symmetric Matrix
    		479(2)
    10.3.5 Singular-Value Decomposition (SVD)
    		481(1)
    10.4 Random Vectors and Matrices
    		482(7)
    10.4.1 Expectations and Other Extensions of Univariate Concepts
    		482(1)
    10.4.2 Partitioning Vectors and Matrices
    		483(2)
    10.4.3 Linear Combinations
    		485(2)
    10.4.4 Mahalanobis Distance, Revisited
    		487(2)
    10.5 Exercises
    		489(2)
    11 The Multivariate Normal (MVN) Distribution
    		491(28)
    11.1 Definition of the MVN
    		491(2)
    11.2 Four Handy Properties of the MVN
    		493(3)
    11.3 Assessing Multinormality
    		496(3)
    11.4 Simulation from the Multivariate Normal Distribution
    		499(5)
    11.4.1 Simulating Independent MVN Variates
    		499(1)
    11.4.2 Simulating Multivariate Time Series
    		500(4)
    11.5 Inferences about a Multinormal Mean Vector
    		504(13)
    11.5.1 Multivariate Central Limit Theorem
    		504(1)
    11.5.2 Hotelling's T2
    		505(6)
    11.5.3 Simultaneous Confidence Statements
    		511(4)
    11.5.4 Interpretation of Multivariate Statistical Significance
    		515(2)
    11.6 Exercises
    		517(2)
    12 Principal Component (EOF) Analysis
    		519(44)
    12.1 Basics of Principal Component Analysis
    		519(12)
    12.1.1 Definition of PCA
    		519(6)
    12.1.2 PCA Based on the Covariance Matrix versus the Correlation Matrix
    		525(2)
    12.1.3 The Varied Terminology of PCA
    		527(1)
    12.1.4 Scaling Conventions in PCA
    		528(2)
    12.1.5 Connections to the Multivariate Normal Distribution
    		530(1)
    12.2 Application of PCA to Geophysical Fields
    		531(7)
    12.2.1 PCA for a Single Field
    		531(2)
    12.2.2 Simultaneous PCA for Multiple Fields
    		533(3)
    12.2.3 Scaling Considerations and Equalization of Variance
    		536(1)
    12.2.4 Domain Size Effects: Buell Patterns
    		536(2)
    12.3 Truncation of the Principal Components
    		538(4)
    12.3.1 Why Truncate the Principal Components?
    		538(1)
    12.3.2 Subjective Truncation Criteria
    		539(1)
    12.3.3 Rules Based on the Size of the Last Retained Eigenvalue
    		539(2)
    12.3.4 Rules Based on Hypothesis-Testing Ideas
    		541(1)
    12.3.5 Rules Based on Structure in the Retained Principal Components
    		542(1)
    12.4 Sampling Properties of the Eigenvalues and Eigenvectors
    		542(5)
    12.4.1 Asymptotic Sampling Results for Multivariate Normal Data
    		542(2)
    12.4.2 Effective Multiplets
    		544(1)
    12.4.3 The North et al. Rule of Thumb
    		545(2)
    12.4.4 Bootstrap Approximations to the Sampling Distributions
    		547(1)
    12.5 Rotation of the Eigenvectors
    		547(7)
    12.5.1 Why Rotate the Eigenvectors?
    		547(1)
    12.5.2 Rotation Mechanics
    		548(3)
    12.5.3 Sensitivity of Orthogonal Rotation to Initial Eigenvector Scaling
    		551(3)
    12.6 Computational Considerations
    		554(1)
    12.6.1 Direct Extraction of Eigenvalues and Eigenvectors from [ S]
    		554(1)
    12.6.2 PCA via SVD
    		555(1)
    12.7 Some Additional Uses of PCA
    		555(7)
    12.7.1 Singular Spectrum Analysis (SSA): Time-Series PCA
    		555(4)
    12.7.2 Principal-Component Regression
    		559(1)
    12.7.3 The Biplot
    		560(2)
    12.8 Exercises
    		562(1)
    13 Canonical Correlation Analysis (CCA)
    		563(20)
    13.1 Basics of CCA
    		563(8)
    13.1.1 Overview
    		563(1)
    13.1.2 Canonical Variates, Canonical Vectors, and Canonical Correlations
    		564(1)
    13.1.3 Some Additional Properties of CCA
    		565(6)
    13.2 CCA Applied to Fields
    		571(5)
    13.2.1 Translating Canonical Vectors to Maps
    		571(1)
    13.2.2 Combining CCA with PCA
    		572(1)
    13.2.3 Forecasting with CCA
    		572(4)
    13.3 Computational Considerations
    		576(4)
    13.3.1 Calculating CCA through Direct Eigendecomposition
    		576(1)
    13.3.2 CCA via SVD
    		577(3)
    13.4 Maximum Covariance Analysis (MCA)
    		580(2)
    13.5 Exercises
    		582(1)
    14 Discrimination and Classification
    		583(20)
    14.1 Discrimination versus Classification
    		583(1)
    14.2 Separating Two Populations
    		583(9)
    14.2.1 Equal Covariance Structure: Fisher's Linear Discriminant
    		583(5)
    14.2.2 Fisher's Linear Discriminant for Multivariate Normal Data
    		588(1)
    14.2.3 Minimizing Expected Cost of Misclassification
    		589(2)
    14.2.4 Unequal Covariances: Quadratic Discrimination
    		591(1)
    14.3 Multiple Discriminant Analysis (MDA)
    		592(5)
    14.3.1 Fisher's Procedure for More Than Two Groups
    		592(3)
    14.3.2 Minimizing Expected Cost of Misclassification
    		595(1)
    14.3.3 Probabilistic Classification
    		596(1)
    14.4 Forecasting with Discriminant Analysis
    		597(2)
    14.5 Alternatives to Classical Discriminant Analysis
    		599(2)
    14.5.1 Discrimination and Classification Using Logistic Regression
    		599(1)
    14.5.2 Discrimination and Classification Using Kernel Density Estimates
    		600(1)
    14.6 Exercises
    		601(2)
    15 Cluster Analysis
    		603(14)
    15.1 Background
    		603(1)
    15.1.1 Cluster Analysis versus Discriminant Analysis
    		603(1)
    15.1.2 Distance Measures and the Distance Matrix
    		603(1)
    15.2 Hierarchical Clustering
    		604(10)
    15.2.1 Agglomerative Methods Using the Distance Matrix
    		604(2)
    15.2.2 Ward's Minimum Variance Method
    		606(1)
    15.2.3 The Dendrogram, or Tree Diagram
    		607(1)
    15.2.4 How Many Clusters?
    		607(5)
    15.2.5 Divisive Methods
    		612(2)
    15.3 Nonhierarchical Clustering
    		614(1)
    15.3.1 The K-Means Method
    		614(1)
    15.3.2 Nucleated Agglomerative Clustering
    		614(1)
    15.3.3 Clustering Using Mixture Distributions
    		615(1)
    15.4 Exercises
    		615(2)
    Appendix A Example Data Sets 617(2)
    Appendix B Probability Tables 619(8)
    Appendix C Answers to Exercises 627(8)
    References 635(26)
    Index 661
    Daniel S. Wilks has been a member of the Atmospheric Sciences faculty at Cornell University since 1987, and is the author of Statistical Methods in the Atmospheric Sciences (2011, Academic Press), which is in its third edition and has been continuously in print since 1995. Research areas include statistical forecasting, forecast postprocessing, and forecast evaluation.
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