Computational Statistics Handbook With MATLAB

As with the bestselling first edition, Computational Statistics Handbook with MATLAB®, Second Edition covers some of the most commonly used contemporary techniques in computational statistics. With a strong, practical focus on implementing the methods, the authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of the algorithms in data analysis. Updated for MATLAB® R2007a and the Statistics Toolbox, Version 6.0, this edition incorporates many additional computational statistics topics. New to the Second Edition • New functions for multivariate normal and multivariate t distributions • Updated information on the new MATLAB functionality for univariate and bivariate histograms, glyphs, and parallel coordinate plots • New content on independent component analysis, nonlinear dimensionality reduction, and multidimensional scaling • New topics on linear classifiers, quadratic classifiers, and voting methods, such as bagging, boosting, and random forests • More methods for unsupervised learning, including model-based clustering and techniques for assessing the results of clustering • A new chapter on parametric models that covers spline regression models, logistic regression, and generalized linear models • Expanded information on smoothers, such as bin smoothing, running mean and line smoothers, and smoothing splines With numerous problems and suggestions for further reading, this accessible text facilitates an understanding of computational statistics concepts and how they are employed in data analysis.

Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statistics Bootstrap Methods Data Partitioning Introduction Cross-Validation Jackknife Better Bootstrap Confidence Intervals Jackknife-after-Bootstrap Probability Density Estimation Introduction Histograms Kernel Density Estimation Finite Mixtures Generating Random Variables Supervised Learning Introduction Bayes’ Decision Theory Evaluating the Classifier Classification Trees Combining Classifiers Unsupervised Learning Introduction Measures of Distance Hierarchical Clustering K-Means Clustering Model-Based Clustering Assessing Cluster Results Parametric Models Introduction Spline Regression Models Logistic Regression Generalized Linear Models Nonparametric models Introduction Some Smoothing Methods Kernel Methods Smoothing Splines Nonparametric Regression—Other Details Regression Trees Additive Models Markov Chain Monte Carlo Methods Introduction Background Metropolis–Hastings Algorithms The Gibbs Sampler Convergence Monitoring Spatial Statistics Introduction Visualizing Spatial Point Processes Exploring First-Order and Second-Order Properties Modeling Spatial Point Processes Simulating Spatial Point Processes Appendix A: Introduction to Matlab What Is MATLAB? Getting Help in MATLAB File and Workspace Management Punctuation in MATLAB Arithmetic Operators Data Constructs in MATLAB Script Files and Functions Control Flow Simple Plotting Contact Information Appendix B: Projection Pursuit Indexes Indexes MATLAB Source Code Appendix C: Matlab Statistics Toolbox Appendix D: Computational Statistics Toolbox Appendix E: Exploratory Data Analysis Toolboxes Introduction EDA Toolbox EDA GUI Toolbox Appendix F: Data Sets Appendix G: NOTATION References INDEX MATLAB Code, Further Reading, and Exercises appear at the end of each chapter.