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Statistical Computing with R

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Series: Chapman &Hall/CRC The R Series.

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

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