Statistical Computing with R, Second Edition SECOND EDITION

Praise for the First Edition: ". . . the book serves as an excellent tutorial on the R language, providing examples that illustrate programming concepts in the context of practical computational problems. The book will be of great interest for all specialists working on computational statistics and Monte Carlo methods for modeling and simulation." – Tzvetan Semerdjiev, Zentralblatt Math Computational statistics and statistical computing are two areas within statistics that may be broadly described as computational, graphical, and numerical approaches to solving statistical problems. Like its bestselling predecessor, Statistical Computing with R, Second Edition covers the traditional core material of these areas with an emphasis on using the R language via an examples-based approach. The new edition is up-to-date with the many advances that have been made in recent years. Features Provides an overview of computational statistics and an introduction to the R computing environment. Focuses on implementation rather than theory. Explores key topics in statistical computing including Monte Carlo methods in inference, bootstrap and jackknife, permutation tests, Markov chain Monte Carlo (MCMC) methods, and density estimation. Includes new sections, exercises and applications as well as new chapters on resampling methods and programming topics. Includes coverage of recent advances including R Studio, the tidyverse, knitr and ggplot2 Accompanied by online supplements available on GitHub including R code for all the exercises as well as tutorials and extended examples on selected topics. Suitable for an introductory course in computational statistics or for self-study, Statistical Computing with R, Second Edition provides a balanced, accessible introduction to computational statistics and statistical computing. About the Author Maria Rizzo is Professor in the Department of Mathematics and Statistics at Bowling Green State University in Bowling Green, Ohio, where she teaches statistics, actuarial science, computational statistics, statistical programming and data science. Prior to joining the faculty at BGSU in 2006, she was Assistant Professor in the Department of Mathematics at Ohio University in Athens, Ohio. Her main research area is energy statistics and distance correlation. She is the software developer and maintainer of the energy package for R. She also enjoys writing books including a forthcoming joint research monograph on energy statistics.

1. Introduction Statistical Computing The R Environment Getting Started with R and RStudioBasic SyntaxUsing the R Online Help SystemDistributions and Statistical TestsFunctions Arrays, Data Frames, and ListsFormula SpecificationsGraphicsIntroduction to ggplotWorkspace and Files Using Scripts Using PackagesUsing R Markdown and knitrExercises 2. Probability and Statistics Review Random Variables and Probability Some Discrete Distributions Some Continuous Distributions Multivariate Normal Distribution Limit Theorems StatisticsBayes’ Theorem and Bayesian StatisticsMarkov Chains 3. Methods for Generating Random Variables Introduction The Inverse Transform Method The Acceptance-Rejection Method Transformation Methods Sums and Mixtures Multivariate Distributions Exercises 4. Generating Random ProcessesStochastic ProcessesBrownian MotionsExercises 5. Visualization of Multivariate Data Introduction Panel Displays Surface Plots and 3D Scatter Plots Contour Plots The Grammar of Graphics and ggplot2 Other 2D Representations of Data Principal Components AnalysisExercises 6. Monte Carlo Integration and Variance Reduction Introduction Monte Carlo IntegrationVariance Reduction Antithetic Variables Control Variates Importance Sampling Stratified Sampling Stratified Importance SamplingExercisesRCode 7. Monte Carlo Methods in Inference Introduction Monte Carlo Methods for Estimation Monte Carlo Methods for Hypothesis Tests ApplicationExercises 8. Bootstrap and JackknifeThe Bootstrap The Jackknife Bootstrap Confidence Intervals Better Bootstrap Confidence Intervals ApplicationExercises 9. Resampling ApplicationsJackknife-after-BootstrapResampling for Regression ModelsInfluenceExercises 10. Permutation Tests Introduction Tests for Equal Distributions Multivariate Tests for Equal Distributions ApplicationExercises 11. Markov Chain Monte Carlo Methods Introduction The Metropolis-Hastings Algorithm The Gibbs Sampler Monitoring Convergence ApplicationExercisesR Code 12. Probability Density Estimation Univariate Density Estimation Kernel Density Estimation Bivariate and Multivariate Density Estimation Other Methods of Density EstimationExercisesR Code 13. Introduction to Numerical Methods in RIntroductionRoot-finding in One DimensionNumerical IntegrationMaximum Likelihood ProblemsApplicationExercises 14. Optimization 401IntroductionOne-dimensional OptimizationMaximum likelihood estimation with mleTwo-dimensional Optimization The EM AlgorithmLinear Programming – The Simplex Method Application Exercises 15. Programming TopicsIntroductionBenchmarking: Comparing the Execution Time of CodeProfilingObject Size, Attributes, and EqualityFinding Source CodeLinking C/C++ Code using RcppApplicationExercises

Maria Rizzo is Professor in the Department of Mathematics and Statistics at Bowling Green State University in Bowling Green, Ohio, where she teaches statistics, actuarial science, computational statistics, statistical programming and data science. Prior to joining the faculty at BGSU in 2006, she was Assistant Professor in the Department of Mathematics at Ohio University in Athens, Ohio. Her main research area is energy statistics and distance correlation. She is the software developer and maintainer of the energy package for R. She also enjoys writing books including a forthcoming joint research monograph on energy statistics.