Contents
Preface to the Second Edition xi Preface to the First Edition xiii 1 Introduction 1
1.1 StatisticalComputing . 1 1.2 TheREnvironment .. 3 1.3 GettingStartedwithRandRStudio . . . . . . . . . . . . . 5 1.4 BasicSyntax 7 1.5 UsingtheROnlineHelpSystem . 9 1.6 DistributionsandStatisticalTests . . . . . . . . . . . . . . . 11 1.7 Functions .. 12 1.8 Arrays,DataFrames,andLists . 13 1.9 FormulaSpecification . 20 1.10Graphics .. 20 1.11Introductiontoggplot 23 1.12WorkspaceandFiles .. 26
1.12.1 TheWorkingDirectory .. 28 1.12.2 ReadingDatafromExternalFiles . . . . . . . . . . . 28 1.12.3 Importing/Exporting.csvFiles . . . . . . . . . . . . . 31
1.13UsingScripts 32
1.14UsingPackages. 1.15 Using R Markdown and knitr . .
2 Probability and Statistics Review
. 33 . 33
37
2.1 RandomVariablesandProbability 37
2.2 SomeDiscreteDistributions 42
2.3 SomeContinuousDistributions .. 45
2.4 MultivariateNormalDistribution 49
2.5 LimitTheorems . 50
2.6 Statistics .. 51
2.7 Bayes Theorem and Bayesian Statistics . . . . .
2.8 MarkovChains
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
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vi Contents
3 Methods for Generating Random Variables 61
3.1 Introduction 61
3.2 TheInverseTransformMethod .. 63 3.2.1 Inverse Transform Method, Continuous Case . . . . . 64
3.2.2 Inverse Transform Method, Discrete Case . . . . . . . 65
3.3 TheAcceptance-RejectionMethod 69
3.4 TransformationMethods .. 71
3.5 SumsandMixtures .. 75
3.6 MultivariateDistributions . 83
3.6.1 MultivariateNormalDistribution. . . . . . . . . . . . 83
3.6.2 MixturesofMultivariateNormals. . . . . . . . . . . . 90
3.6.3 WishartDistribution. 92
3.6.4 Uniform Distribution on the d-Sphere . . . . . . . . . 93
Exercises .. 96
4 Generating Random Processes 99
4.1 StochasticProcesses .. 99
4.1.1 PoissonProcesses 99
4.1.2 RenewalProcesses .. 104
4.1.3 SymmetricRandomWalk . 105
4.2 BrownianMotion 109
Exercises .. 112
5 Visualization of Multivariate Data 115
5.1 Introduction 115
5.2 PanelDisplays .. 115
5.3 CorrelationPlots. 118
5.4 SurfacePlotsand3DScatterPlots . . . . . . . . . . . . . . 120
5.4.1 SurfacePlots .. 121
5.4.2 Three-dimensional Scatterplot . . . . . . . . . . . . . 124
5.5 ContourPlots .. 126
5.6 Other2DRepresentationsofData 129
5.6.1 AndrewsCurves 129
5.6.2 ParallelCoordinatePlots . 132
5.6.3 Segments, Stars, and Other Representations . . . . . . 133
5.7 PrincipalComponentsAnalysis . 135
5.8 OtherApproachestoDataVisualization . . . . . . . . . . . 141
5.9 AdditionalResources . 143
Exercises .. 143
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
Created from ualberta on 2021-03-06 10:34:03.
Copyright 2019. CRC Press LLC. All rights reserved.
Contents vii
6 Monte Carlo Integration and Variance Reduction 147
6.1 Introduction 147
6.2 MonteCarloIntegration .. 147 6.2.1 SimpleMonteCarloEstimator . . . . . . . . . . . . . 148 6.2.2 VarianceandEfficiency .. 152
6.3 VarianceReduction .. 154
6.4 AntitheticVariables .. 155
6.5 ControlVariates . 159
6.5.1 Antithetic Variate as Control Variate . . . . . . . . . . 162
6.5.2 SeveralControlVariates.. 163
6.5.3 ControlVariatesandRegression . . . . . . . . . . . . 163
6.6 ImportanceSampling . 168
6.7 StratifiedSampling .. 173
6.8 StratifiedImportanceSampling . 176
Exercises .. 178 RCode 181
7 Monte Carlo Methods in Inference 183
7.1 Introduction 183
7.2 MonteCarloMethodsforEstimation . . . . . . . . . . . . . 184 7.2.1 Monte Carlo Estimation and Standard Error . . . . . 184 7.2.2 EstimationofMSE.. 185 7.2.3 EstimatingaConfidenceLevel . . . . . . . . . . . . . 188
7.3 MonteCarloMethodsforHypothesisTests . . . . . . . . . . 192 7.3.1 EmpiricalTypeIErrorRate .. 193 7.3.2 PowerofaTest. 197 7.3.3 PowerComparisons . 200
7.4 Application: Count Five Test for Equal Variance . . . . . . 204
Exercises .. 209
8 Bootstrap and Jackknife 213
8.1 TheBootstrap .. 213 8.1.1 Bootstrap Estimation of Standard Error . . . . . . . . 215 8.1.2 BootstrapEstimationofBias .. 217
8.2 TheJackknife .. 220
8.3 BootstrapConfidenceIntervals .. 224
8.3.1 The Standard Normal Bootstrap Confidence Interval . 224
8.3.2 The Basic Bootstrap Confidence Interval . . . . . . . . 225
8.3.3 The Percentile Bootstrap Confidence Interval . . . . . 226
8.3.4 TheBootstraptInterval.. 228
8.4 BetterBootstrapConfidenceIntervals . . . . . . . . . . . . . 231
8.5 Application:CrossValidation 235
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
Created from ualberta on 2021-03-06 10:34:03.
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viii
Contents
9
Exercises .. 239 Resampling Applications 243
9.1 Jackknife-after-Bootstrap .. 243
9.2 ResamplingforRegressionModels 246 9.2.1 ResamplingCases .. 250 9.2.2 ResamplingErrors(ModelBased) . . . . . . . . . . . 254
9.3 Influence .. 260
9.3.1 Empirical Influence Values for a Statistic . . . . . . . 260
9.3.2 Jackknife-after-Bootstrap Plots . . . . . . . . . . . . . 261
Exercises .. 263
10 Permutation Tests 265
10.1Introduction 265 10.2TestsforEqualDistributions 269 10.3 Multivariate Tests for Equal Distributions . . . . . . . . . . 272
10.3.1 NearestNeighborTests .. 273
10.3.2 Energy Test for Equal Distributions . . . . . . . . . . 281 10.4 Application:DistanceCorrelation . . . . . . . . . . . . . . . 287 Exercises .. 294
11 Markov Chain Monte Carlo Methods 297
11.1Introduction 297 11.1.1 Integration Problems in Bayesian Inference . . . . . . 297 11.1.2 Markov Chain Monte Carlo Integration . . . . . . . . 298
11.2 TheMetropolis-HastingsAlgorithm . . . . . . . . . . . . . . 299 11.2.1 Metropolis-HastingsSampler . . . . . . . . . . . . . . 300 11.2.2 TheMetropolisSampler.. 310 11.2.3 RandomWalkMetropolis . 310 11.2.4 TheIndependenceSampler 316
11.3TheGibbsSampler .. 318 11.4MonitoringConvergence .. 322 11.4.1 WhyMonitorConvergence 322 11.4.2 Methods for Monitoring Convergence . . . . . . . . . . 323 11.4.3 TheGelman-RubinMethod 323 11.5 Application:ChangePointAnalysis . . . . . . . . . . . . . . 327 Exercises .. 333 RCode 335
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
Created from ualberta on 2021-03-06 10:34:03.
Copyright 2019. CRC Press LLC. All rights reserved.
Contents ix 12 Probability Density Estimation 337
12.1UnivariateDensityEstimation .. 337 12.1.1 Histograms 338 12.1.2 Frequency Polygon Density Estimate . . . . . . . . . . 345 12.1.3 TheAveragedShiftedHistogram . . . . . . . . . . . . 347
12.2KernelDensityEstimation . 351
12.3 Bivariate and Multivariate Density Estimation . . . . . . . . 361 12.3.1 BivariateFrequencyPolygon .. 361 12.3.2 BivariateASH . 364 12.3.3 Multidimensional Kernel Methods . . . . . . . . . . . 366
12.4 OtherMethodsofDensityEstimation . . . . . . . . . . . . . 369
Exercises .. 370 RCode 373
13 Introduction to Numerical Methods in R 375
13.1Introduction 375 13.2Root-findinginOneDimension . 383 13.3NumericalIntegration . 386 13.4MaximumLikelihoodProblems.. 391 13.5 Application: Evaluating an Expected Value . . . . . . . . . . 394 Exercises .. 398
14 Optimization 401
14.1Introduction 401 14.2One-dimensionalOptimization .. 402 14.3 Maximum Likelihood Estimation with mle . . . . . . . . . . 403 14.4Two-dimensionalOptimization .. 405 14.5TheEMAlgorithm .. 409 14.6 Linear Programming The Simplex Method . . . . . . . . . 411 14.7Application:GameTheory . 413 Exercises .. 417
15 Programming Topics 419
15.1Introduction 419 15.2 Benchmarking: Comparing the Execution Time of Code . . . 419 15.2.1 Using the microbenchmark Package . . . . . . . . . . 420 15.2.2 UsingtherbenchmarkPackage . . . . . . . . . . . . . 423 15.3Profiling .. 425 15.4 ObjectSize,Attributes,andEquality . . . . . . . . . . . . . 427 15.4.1 ObjectSize 427 15.4.2 AttributesofObjects. 428
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
Created from ualberta on 2021-03-06 10:34:03.
Copyright 2019. CRC Press LLC. All rights reserved.
x
Contents
15.4.3 ComparingObjectsforEquality . . . . . . . . . . . . 429 15.5FindingSourceCode . 430 15.5.1 FindingRFunctionCode . 430 15.5.2 Methods.. 431 15.5.3 MethodsandFunctionsinPackages . . . . . . . . . . 432 15.5.4 CompiledCode. 433 15.6LinkingC/C++CodeUsingRcpp 434 15.7Application:BaseballData . 438 Exercises .. 442
Notation 445 Bibliography 447 Index 469
Rizzo, Maria L.. Statistical Computing with R, Second Edition, CRC Press LLC, 2019. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ualberta/detail.action?docID=5731927.
Created from ualberta on 2021-03-06 10:34:03.
Copyright 2019. CRC Press LLC. All rights reserved.
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