Statistical Computing With R

by Rizzo; Maria L.

• ISBN13: 9781584885450
• ISBN10: 1584885459
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-11-15
• Publisher: Chapman & Hall/

Summary

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 Rcovers 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, thevisualization 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.

Author Biography

Maria L. Rizzo Bowling Green State University, Bowling Green, Ohio, U.S.A.

Table of Contents

Preface	p. xv
Introduction	p. 1
Computational Statistics and Statistical Computing	p. 1
The R Environment	p. 3
Getting Started with R	p. 4
Using the R Online Help System	p. 7
Functions	p. 8
Arrays, Data Frames, and Lists	p. 9
Workspace and Files	p. 15
Using Scripts	p. 17
Using Packages	p. 18
Graphics	p. 19
Probability and Statistics Review	p. 21
Random Variables and Probability	p. 21
Some Discrete Distributions	p. 25
Some Continuous Distributions	p. 29
Multivariate Normal Distribution	p. 33
Limit Theorems	p. 35
Statistics	p. 35
Bayes' Theorem and Bayesian Statistics	p. 40
Markov Chains	p. 42
Methods for Generating Random Variables	p. 47
Introduction	p. 47
The Inverse Transform Method	p. 49
The Acceptance-Rejection Method	p. 55
Transformation Methods	p. 58
Sums and Mixtures	p. 61
Multivariate Distributions	p. 69
Stochastic Processes	p. 82
Exercises	p. 94
Visualization of Multivariate Data	p. 97
Introduction	p. 97
Panel Displays	p. 97
Surface Plots and 3D Scatter Plots	p. 100
Contour Plots	p. 106
Other 2D Representations of Data	p. 110
Other Approaches to Data Visualization	p. 115
Exercises	p. 116
Monte Carlo Integration and Variance Reduction	p. 119
Introduction	p. 119
Monte Carlo Integration	p. 119
Variance Reduction	p. 126
Antithetic Variables	p. 128
Control Variates	p. 132
Importance Sampling	p. 139
Stratified Sampling	p. 144
Stratified Importance Sampling	p. 147
Exercises	p. 149
R Code	p. 152
Monte Carlo Methods in Inference	p. 153
Introduction	p. 153
Monte Carlo Methods for Estimation	p. 154
Monte Carlo Methods for Hypothesis Tests	p. 162
Application	p. 174
Exercises	p. 180
Bootstrap and Jackknife	p. 183
The Bootstrap	p. 183
The Jackknife	p. 190
Jackknife-after-Bootstrap	p. 195
Bootstrap Confidence Intervals	p. 197
Better Bootstrap Confidence Intervals	p. 203
Application	p. 207
Exercises	p. 212
Permutation Tests	p. 215
Introduction	p. 215
Tests for Equal Distributions	p. 219
Multivariate Tests for Equal Distributions	p. 222
Application	p. 235
Exercises	p. 242
Markov Chain Monte Carlo Methods	p. 245
Introduction	p. 245
The Metropolis-Hastings Algorithm	p. 247
The Gibbs Sampler	p. 263
Monitoring Convergence	p. 266
Application	p. 271
Exercises	p. 277
R Code	p. 279
Probability Density Estimation	p. 281
Univariate Density Estimation	p. 281
Kernel Density Estimation	p. 296
Bivariate and Multivariate Density Estimation	p. 305
Other Methods of Density Estimation	p. 314
Exercises	p. 314
R Code	p. 317
Numerical Methods in R	p. 319
Introduction	p. 319
Root-finding in One Dimension	p. 326
Numerical Integration	p. 330
Maximum Likelihood Problems	p. 335
One-dimensional Optimization	p. 338
Two-dimensional Optimization	p. 342
The EM Algorithm	p. 345
Linear Programming - The Simplex Method	p. 348
Application	p. 349
Exercises	p. 353
Notation	p. 355
Working with Data Frames and Arrays	p. 357
Resampling and Data Partitioning	p. 357
Subsetting and Reshaping Data	p. 360
Data Entry and Data Analysis	p. 364
References	p. 375
Index	p. 395
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