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2nd Edition

Statistical Computing with R, Second Edition



ISBN 9781466553323
Published March 6, 2019 by Chapman and Hall/CRC
504 Pages 150 B/W Illustrations

 
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Book Description

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

...
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Author(s)

Biography

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.  

Reviews

Praise for the First Edition:
"… 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, 2008, Vol. 1137

"Statistical computing and computational statistics are two areas of statistics described as computational, graphical, and numerical approaches to solving statistical problems. Statistical Computing with R comprises, thorough and examples-based approach, the conventional core material of computational statistics with an emphasis on R... This book includes standard statistical computing topics using the R language... All examples in the text are realised in R. Software is actively maintained, it has good connectivity to various types of data and other systems, and it is versatile. In addition, R is very stable and reliable... The book also includes exercises and applications in all chapters, as well as coverage of recent advances including R Studio. Many examples are included, fully implemented in the R statistical computing environment, and the R code for the examples can be downloaded from the author’s website. Most examples and exercises apply datasets accessible in the R distribution or simulated data. The author, Maria L. Rizzo, is a Full Professor at the Department of Mathematics and Statistics of Bowling Green State University (US) and is an expert on Applied Statistics, Statistical Computing, and Energy Statistics... After finishing the book, I feel that it is a well-written text useful for biostatisticians and graduate teachers, principally because it is written by a leading expert who is engaged in statistical modelling and methodological developments and applications in the real world. In my opinion, the book is a must-have for the interested biostatistician audience."
- Luca Bertolaccini, ISCB December 2019

"...This book tries to keep a balance between theory and practice, with more focus on the latter...also provides plenty of R codes to help the readers practice what they learned from the book. As stated in the preface, the targeted readers of this book are graduate students and advanced undergraduates with preparation in the relevant mathematics foundations. From this point of view, the content of the book fits well to the anticipated audience...I really appreciate the section on “finding source code” in Chapter 15. A lot of the libraries in R are written in C or Fortran. Occasionally, we need to dig into those codes and make changes to suit our needs. It is very helpful in our daily research to be able to find the source code and compile the changes...Finally, I would like to give credit to the author on making their code available on github. This makes it convenient for readers to try the code themselves without lots of typing. It also allows the authors to easily make updated code available to readers."
- Ling Leng, JASA, September 2020

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