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Statistical Computing with R, Second Edition (Hardcover, 3rd Edition)
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Statistical Computing with R, Second Edition (Hardcover, 3rd Edition)
Series: Chapman & Hall/CRC The R Series
Expected to ship within 21 working days
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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.
Table of Contents
1. Introduction
Statistical Computing
The R Environment
Getting Started with R and RStudio
Basic Syntax
Using the R Online Help System
Distributions and Statistical Tests
Functions
Arrays, Data Frames, and Lists
Formula Specifications
Graphics Introduction to ggplot
Workspace and Files
Using Scripts
Using Packages
Using R Markdown and knitr
Exercises
2. 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
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 Processes
Stochastic Processes
Brownian Motions
Exercises
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 Analysis
Exercises
6. Monte Carlo Integration and Variance Reduction
Introduction
Monte Carlo Integration
Variance Reduction
Antithetic Variables
Control Variates
Importance Sampling
Stratified Sampling
Stratified Importance Sampling
Exercises
RCode
7. Monte Carlo Methods in Inference
Introduction
Monte Carlo Methods for Estimation
Monte Carlo Methods for Hypothesis Tests
Application
Exercises
8. Bootstrap and Jackknife
The Bootstrap
The Jackknife
Bootstrap Confidence Intervals
Better Bootstrap Confidence Intervals
Application
Exercises
9. Resampling Applications
Jackknife-after-Bootstrap
Resampling for Regression Models
Influence
Exercises
10. Permutation Tests
Introduction
Tests for Equal Distributions
Multivariate Tests for Equal Distributions
Application
Exercises
11. Markov Chain Monte Carlo Methods
Introduction
The Metropolis-Hastings Algorithm
The Gibbs Sampler
Monitoring Convergence
Application
Exercises
R Code
12. Probability Density Estimation
Univariate Density Estimation
Kernel Density Estimation
Bivariate and Multivariate Density Estimation
Other Methods of Density Estimation
Exercises
R Code
13. Introduction to Numerical Methods in R
Introduction
Root-finding in One Dimension
Numerical Integration
Maximum Likelihood Problems
Application
Exercises
14. Optimization 401
Introduction
One-dimensional Optimization
Maximum likelihood estimation with mle
Two-dimensional Optimization
The EM Algorithm
Linear Programming – The Simplex Method
Application
Exercises
15. Programming Topics
Introduction
Benchmarking: Comparing the Execution Time of Code
Profiling
Object Size, Attributes, and Equality
Finding Source Code
Linking C/C++ Code using Rcpp
Application
Exercises
General
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