Statistical Computing with R, Second Edition

Chapter 1: IntroductionStatistical 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

Chapter 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

Chapter 3: Methods for Generating Random Variables

• • Introduction
• • The Inverse Transform Method
• • The Acceptance-Rejection Method
• • Transformation Methods
• • Sums and Mixtures
• • Multivariate Distributions
• • Exercises

Chapter 4: Generating Random Processes

• • Stochastic Processes
• • Brownian Motions
• • Exercises

Chapter 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

Chapter 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

Chapter 7: Monte Carlo Methods in Inference

• • Introduction
• • Monte Carlo Methods for Estimation
• • Monte Carlo Methods for Hypothesis Tests
• • Application
• • Exercises

Chapter 8: Bootstrap and Jackknife

• • The Bootstrap
• • The Jackknife
• • Bootstrap Confidence Intervals
• • Better Bootstrap Confidence Intervals
• • Application
• • Exercises

Chapter 9: Resampling Applications

• • Jackknife-after-Bootstrap
• • Resampling for Regression Models
• • Influence
• • Exercises

Chapter 10: Permutation Tests

• • Introduction
• • Tests for Equal Distributions
• • Multivariate Tests for Equal Distributions
• • Application
• • Exercises

Chapter 11: Markov Chain Monte Carlo Methods

• • Introduction
• • The Metropolis-Hastings Algorithm
• • The Gibbs Sampler
• • Monitoring Convergence
• • Application
• • Exercises
• • R Code

Chapter 12: Probability Density Estimation

• • Univariate Density Estimation
• • Kernel Density Estimation
• • Bivariate and Multivariate Density Estimation
• • Other Methods of Density Estimation
• • Exercises
• • R Code

Chapter 13: Introduction to Numerical Methods in R

• • Introduction
• • Root-finding in One Dimension
• • Numerical Integration
• • Maximum Likelihood Problems
• • Application
• • Exercises

Chapter 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

Chapter 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