Statistical Computing with R

✍ Scribed by Maria L. Rizzo

• Year: 2019
• Tongue: English
• Leaves: 491
• Edition: 2
• Category: Library

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface to the Second Edition
Preface to the First Edition
1: Introduction
1.1 Statistical Computing
1.2 The R Environment
1.3 Getting Started with R and RStudio
1.4 Basic Syntax
1.5 Using the R Online Help System
1.6 Distributions and Statistical Tests
1.7 Functions
1.8 Arrays, Data Frames, and Lists
1.9 Formula Specification
1.10 Graphics
1.11 Introduction to ggplot
1.12 Workspace and Files
1.12.1 The Working Directory
1.12.2 Reading Data from External Files
1.12.3 Importing/Exporting .csv Files
1.13 Using Scripts
1.14 Using Packages
1.15 Using R Markdown and knitr
2: Probability and Statistics Review
2.1 Random Variables and Probability
2.2 Some Discrete Distributions
2.3 Some Continuous Distributions
2.4 Multivariate Normal Distribution
2.5 Limit Theorems
2.6 Statistics
2.7 Bayes’ Theorem and Bayesian Statistics
2.8 Markov Chains
3: Methods for Generating Random Variables
3.1 Introduction
3.2 The Inverse Transform Method
3.2.1 Inverse Transform Method, Continuous Case
3.2.2 Inverse Transform Method, Discrete Case
3.3 The Acceptance-Rejection Method
3.4 Transformation Methods
3.5 Sums and Mixtures
3.6 Multivariate Distributions
3.6.1 Multivariate Normal Distribution
3.6.2 Mixtures of Multivariate Normals
3.6.3 Wishart Distribution
3.6.4 Uniform Distribution on the d-Sphere
Exercises
4: Generating Random Processes
4.1 Stochastic Processes
4.1.1 Poisson Processes
4.1.2 Renewal Processes
4.1.3 Symmetric Random Walk
4.2 Brownian Motion
Exercises
5: Visualization of Multivariate Data
5.1 Introduction
5.2 Panel Displays
5.3 Correlation Plots
5.4 Surface Plots and 3D Scatter Plots
5.4.1 Surface Plots
5.4.2 Three-dimensional Scatterplot
5.5 Contour Plots
5.6 Other 2D Representations of Data
5.6.1 Andrews Curves
5.6.2 Parallel Coordinate Plots
5.6.3 Segments, Stars, and Other Representations
5.7 Principal Components Analysis
5.8 Other Approaches to Data Visualization
5.9 Additional Resources
Exercises
6: Monte Carlo Integration and Variance Reduction
6.1 Introduction
6.2 Monte Carlo Integration
6.2.1 Simple Monte Carlo Estimator
6.2.2 Variance and Efficiency
6.3 Variance Reduction
6.4 Antithetic Variables
6.5 Control Variates
6.5.1 Antithetic Variate as Control Variate
6.5.2 Several Control Variates
6.5.3 Control Variates and Regression
6.6 Importance Sampling
6.7 Stratified Sampling
6.8 Stratified Importance Sampling
Exercises
R Code
7: Monte Carlo Methods in Inference
7.1 Introduction
7.2 Monte Carlo Methods for Estimation
7.2.1 Monte Carlo Estimation and Standard Error
7.2.2 Estimation of MSE
7.2.3 Estimating a Confidence Level
7.3 Monte Carlo Methods for Hypothesis Tests
7.3.1 Empirical Type I Error Rate
7.3.2 Power of a Test
7.3.3 Power Comparisons
7.4 Application: “Count Five” Test for Equal Variance
Exercises
8: Bootstrap and Jackknife
8.1 The Bootstrap
8.1.1 Bootstrap Estimation of Standard Error
8.1.2 Bootstrap Estimation of Bias
8.2 The Jackknife
8.3 Bootstrap Confidence Intervals
8.3.1 The Standard Normal Bootstrap Confidence Interval
8.3.2 The Basic Bootstrap Confidence Interval
8.3.3 The Percentile Bootstrap Confidence Interval
8.3.4 The Bootstrap t Interval
8.4 Better Bootstrap Confidence Intervals
8.5 Application: Cross Validation
Exercises
9: Resampling Applications
9.1 Jackknife-after-Bootstrap
9.2 Resampling for Regression Models
9.2.1 Resampling Cases
9.2.2 Resampling Errors (Model Based)
9.3 Influence
9.3.1 Empirical Influence Values for a Statistic
9.3.2 Jackknife-after-Bootstrap Plots
Exercises
10: Permutation Tests
10.1 Introduction
10.2 Tests for Equal Distributions
10.3 Multivariate Tests for Equal Distributions
10.3.1 Nearest Neighbor Tests
10.3.2 Energy Test for Equal Distributions
10.4 Application: Distance Correlation
Exercises
11: Markov Chain Monte Carlo Methods
11.1 Introduction
11.1.1 Integration Problems in Bayesian Inference
11.1.2 Markov Chain Monte Carlo Integration
11.2 The Metropolis-Hastings Algorithm
11.2.1 Metropolis-Hastings Sampler
11.2.2 The Metropolis Sampler
11.2.3 Random Walk Metropolis
11.2.4 The Independence Sampler
11.3 The Gibbs Sampler
11.4 Monitoring Convergence
11.4.1 Why Monitor Convergence
11.4.2 Methods for Monitoring Convergence
11.4.3 The Gelman-Rubin Method
11.5 Application: Change Point Analysis
Exercises
R Code
12: Probability Density Estimation
12.1 Univariate Density Estimation
12.1.1 Histograms
12.1.2 Frequency Polygon Density Estimate
12.1.3 The Averaged Shifted Histogram
12.2 Kernel Density Estimation
12.3 Bivariate and Multivariate Density Estimation
12.3.1 Bivariate Frequency Polygon
12.3.2 Bivariate ASH
12.3.3 Multidimensional Kernel Methods
12.4 Other Methods of Density Estimation
Exercises
R Code
13: Introduction to Numerical Methods in R
13.1 Introduction
13.2 Root-finding in One Dimension
13.3 Numerical Integration
13.4 Maximum Likelihood Problems
13.5 Application: Evaluating an Expected Value
Exercises
14: Optimization
14.1 Introduction
14.2 One-dimensional Optimization
14.3 Maximum Likelihood Estimation with mle
14.4 Two-dimensional Optimization
14.5 The EM Algorithm
14.6 Linear Programming – The Simplex Method
14.7 Application: Game Theory
Exercises
15: Programming Topics
15.1 Introduction
15.2 Benchmarking: Comparing the Execution Time of Code
15.2.1 Using the microbenchmark Package
15.2.2 Using the rbenchmark Package
15.3 Profiling
15.4 Object Size, Attributes, and Equality
15.4.1 Object Size
15.4.2 Attributes of Objects
15.4.3 Comparing Objects for Equality
15.5 Finding Source Code
15.5.1 Finding R Function Code
15.5.2 Methods
15.5.3 Methods and Functions in Packages
15.5.4 Compiled Code
15.6 Linking C/C++ Code Using Rcpp
15.7 Application: Baseball Data
Exercises
Notation
Bibliography
Index