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| Preface | |
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| Introduction | |
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| Computational Statistics and Statistical Computing | |
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| The R Environment | |
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| Getting Started with R | |
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| Using the R Online Help System | |
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| Functions | |
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| Arrays, Data Frames, and Lists | |
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| Workspace and Files | |
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| Using Scripts | |
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| Using Packages | |
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| Graphics | |
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| Probability and Statistics Review | |
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| Random Variables and Probability | |
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| Some Discrete Distributions | |
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| Some Continuous Distributions | |
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| Multivariate Normal Distribution | |
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| Limit Theorems | |
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| Statistics | |
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| Bayes' Theorem and Bayesian Statistics | |
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| Markov Chains | |
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| Methods for Generating Random Variables | |
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| Introduction | |
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| The Inverse Transform Method | |
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| The Acceptance-Rejection Method | |
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| Transformation Methods | |
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| Sums and Mixtures | |
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| Multivariate Distributions | |
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| Stochastic Processes | |
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| Exercises | |
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| Visualization of Multivariate Data | |
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| Introduction | |
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| Panel Displays | |
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| Surface Plots and 3D Scatter Plots | |
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| Contour Plots | |
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| Other 2D Representations of Data | |
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| Other Approaches to Data Visualization | |
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| Exercises | |
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| Monte Carlo Integration and Variance Reduction | |
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| Introduction | |
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| Monte Carlo Integration | |
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| Variance Reduction | |
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| Antithetic Variables | |
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| Control Variates | |
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| Importance Sampling | |
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| Stratified Sampling | |
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| Stratified Importance Sampling | |
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| Exercises | |
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| R Code | |
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| Monte Carlo Methods in Inference | |
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| Introduction | |
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| Monte Carlo Methods for Estimation | |
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| Monte Carlo Methods for Hypothesis Tests | |
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| Application | |
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| Exercises | |
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| Bootstrap and Jackknife | |
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| The Bootstrap | |
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| The Jackknife | |
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| Jackknife-after-Bootstrap | |
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| Bootstrap Confidence Intervals | |
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| Better Bootstrap Confidence Intervals | |
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| Application | |
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| Exercises | |
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| Permutation Tests | |
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| Introduction | |
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| Tests for Equal Distributions | |
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| Multivariate Tests for Equal Distributions | |
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| Application | |
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| Exercises | |
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| Markov Chain Monte Carlo Methods | |
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| Introduction | |
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| The Metropolis-Hastings Algorithm | |
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| The Gibbs Sampler | |
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| Monitoring Convergence | |
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| Application | |
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| Exercises | |
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| R Code | |
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| Probability Density Estimation | |
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| Univariate Density Estimation | |
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| Kernel Density Estimation | |
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| Bivariate and Multivariate Density Estimation | |
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| Other Methods of Density Estimation | |
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| Exercises | |
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| R Code | |
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| Numerical Methods in R | |
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| Introduction | |
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| Root-finding in One Dimension | |
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| Numerical Integration | |
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| Maximum Likelihood Problems | |
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| One-dimensional Optimization | |
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| Two-dimensional Optimization | |
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| The EM Algorithm | |
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| Linear Programming - The Simplex Method | |
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| Application | |
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| Exercises | |
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| Notation | |
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| Working with Data Frames and Arrays | |
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| Resampling and Data Partitioning | |
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| Subsetting and Reshaping Data | |
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| Data Entry and Data Analysis | |
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| References | |
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| Index | |