Statistical Computing with R, Second Edition

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