Statistical Computing with R
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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 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
Editorial Reviews
". . . 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, in Zentralblatt Math, 2008, Vol. 1137
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| Cross Platform | May 10, 2011 | R Code and Errata | click on http://personal.bgsu.edu/~mrizzo/SCR.htm |
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