2nd Edition

Statistical Computing with R, Second Edition

By Maria L. Rizzo Copyright 2019
    490 Pages 150 B/W Illustrations
    by Chapman & Hall

    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.   

     

     

     

     

     

     

     

     

     

     

    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

    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.  

    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