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What is included with this book?
Preface | p. xv |
Introduction | p. 1 |
Computational Statistics and Statistical Computing | p. 1 |
The R Environment | p. 3 |
Getting Started with R | p. 4 |
Using the R Online Help System | p. 7 |
Functions | p. 8 |
Arrays, Data Frames, and Lists | p. 9 |
Workspace and Files | p. 15 |
Using Scripts | p. 17 |
Using Packages | p. 18 |
Graphics | p. 19 |
Probability and Statistics Review | p. 21 |
Random Variables and Probability | p. 21 |
Some Discrete Distributions | p. 25 |
Some Continuous Distributions | p. 29 |
Multivariate Normal Distribution | p. 33 |
Limit Theorems | p. 35 |
Statistics | p. 35 |
Bayes' Theorem and Bayesian Statistics | p. 40 |
Markov Chains | p. 42 |
Methods for Generating Random Variables | p. 47 |
Introduction | p. 47 |
The Inverse Transform Method | p. 49 |
The Acceptance-Rejection Method | p. 55 |
Transformation Methods | p. 58 |
Sums and Mixtures | p. 61 |
Multivariate Distributions | p. 69 |
Stochastic Processes | p. 82 |
Exercises | p. 94 |
Visualization of Multivariate Data | p. 97 |
Introduction | p. 97 |
Panel Displays | p. 97 |
Surface Plots and 3D Scatter Plots | p. 100 |
Contour Plots | p. 106 |
Other 2D Representations of Data | p. 110 |
Other Approaches to Data Visualization | p. 115 |
Exercises | p. 116 |
Monte Carlo Integration and Variance Reduction | p. 119 |
Introduction | p. 119 |
Monte Carlo Integration | p. 119 |
Variance Reduction | p. 126 |
Antithetic Variables | p. 128 |
Control Variates | p. 132 |
Importance Sampling | p. 139 |
Stratified Sampling | p. 144 |
Stratified Importance Sampling | p. 147 |
Exercises | p. 149 |
R Code | p. 152 |
Monte Carlo Methods in Inference | p. 153 |
Introduction | p. 153 |
Monte Carlo Methods for Estimation | p. 154 |
Monte Carlo Methods for Hypothesis Tests | p. 162 |
Application | p. 174 |
Exercises | p. 180 |
Bootstrap and Jackknife | p. 183 |
The Bootstrap | p. 183 |
The Jackknife | p. 190 |
Jackknife-after-Bootstrap | p. 195 |
Bootstrap Confidence Intervals | p. 197 |
Better Bootstrap Confidence Intervals | p. 203 |
Application | p. 207 |
Exercises | p. 212 |
Permutation Tests | p. 215 |
Introduction | p. 215 |
Tests for Equal Distributions | p. 219 |
Multivariate Tests for Equal Distributions | p. 222 |
Application | p. 235 |
Exercises | p. 242 |
Markov Chain Monte Carlo Methods | p. 245 |
Introduction | p. 245 |
The Metropolis-Hastings Algorithm | p. 247 |
The Gibbs Sampler | p. 263 |
Monitoring Convergence | p. 266 |
Application | p. 271 |
Exercises | p. 277 |
R Code | p. 279 |
Probability Density Estimation | p. 281 |
Univariate Density Estimation | p. 281 |
Kernel Density Estimation | p. 296 |
Bivariate and Multivariate Density Estimation | p. 305 |
Other Methods of Density Estimation | p. 314 |
Exercises | p. 314 |
R Code | p. 317 |
Numerical Methods in R | p. 319 |
Introduction | p. 319 |
Root-finding in One Dimension | p. 326 |
Numerical Integration | p. 330 |
Maximum Likelihood Problems | p. 335 |
One-dimensional Optimization | p. 338 |
Two-dimensional Optimization | p. 342 |
The EM Algorithm | p. 345 |
Linear Programming - The Simplex Method | p. 348 |
Application | p. 349 |
Exercises | p. 353 |
Notation | p. 355 |
Working with Data Frames and Arrays | p. 357 |
Resampling and Data Partitioning | p. 357 |
Subsetting and Reshaping Data | p. 360 |
Data Entry and Data Analysis | p. 364 |
References | p. 375 |
Index | p. 395 |
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