Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditional core material of computational statistics, with an emphasis on using the R language via an examples-based approach. Suitable for an introductory course in computational statistics or for self-study, it includes R code for all examples and R notes to help explain the R programming concepts. After an overview of computational statistics and an introduction to the R computing environment, the book reviews some basic concepts in probability and classical statistical inference. Each subsequent chapter explores a specific topic in computational statistics. These chapters cover the simulation of random variables from probability distributions, the visualization of multivariate data, Monte Carlo integration and variance reduction methods, Monte Carlo methods in inference, bootstrap and jackknife, permutation tests, Markov chain Monte Carlo (MCMC) methods, and density estimation. The final chapter presents a selection of examples that illustrate the application of numerical methods using R functions. Focusing on implementation rather than theory, this text serves as a balanced, accessible introduction to computational statistics and statistical computing.

Table of Contents:
preface Introduction Computational Statistics and Statistical Computing The R Environment Getting Started with R Using the R Online Help System Functions Arrays, Data Frames, and Lists Workspace and Files Using Scripts Using Packages Graphics Probability and Statistics Review Random Variables and Probability Some Discrete Distributions Some Continuous Distributions Multivariate Normal Distribution Limit Theorems Statistics Bayes’ Theorem and Bayesian Statistics Markov Chains Methods for Generating Random Variables Introduction The Inverse Transform Method The Acceptance-Rejection Method Transformation Methods Sums and Mixtures Multivariate Distributions Stochastic Processes Exercises Visualization of Multivariate Data Introduction Panel Displays Surface Plots and 3D Scatter Plots Contour Plots Other 2D Representations of Data Other Approaches to Data Visualization Exercises Monte Carlo Integration and Variance Reduction Introduction Monte Carlo Integration Variance Reduction Antithetic Variables Control Variates Importance Sampling Stratified Sampling Stratified Importance Sampling Exercises R Code Monte Carlo Methods in Inference Introduction Monte Carlo Methods for Estimation Monte Carlo Methods for Hypothesis Tests Application Exercises Bootstrap and Jackknife The Bootstrap The Jackknife Jackknife-after-Bootstrap Bootstrap Confidence Intervals Better Bootstrap Confidence Intervals Application Exercises Permutation Tests Introduction Tests for Equal Distributions Multivariate Tests for Equal Distributions Application Exercises Markov Chain Monte Carlo Methods Introduction The Metropolis–Hastings Algorithm The Gibbs Sampler Monitoring Convergence Application Exercises R Code Probability Density Estimation Univariate Density Estimation Kernel Density Estimation Bivariate and Multivariate Density Estimation Other Methods of Density Estimation Exercises R Code Numerical Methods in R Introduction Root-Finding in One Dimension Numerical Integration Maximum Likelihood Problems 1D Optimization 2D Optimization The EM Algorithm Linear Programming—The Simplex Method Application Exercises APPENDIX A: Notation APPENDIX B: Working with Data Frames and Arrays Resampling and Data Partitioning Subsetting and Reshaping Data Data Entry and Data Analysis References Index