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Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models.
Key features:
* Integrates R basics with statistical concepts
* Provides graphical presentations inclusive of mathematical expressions
* Aids understanding of limit theorems of probability with and without the simulation approach
* Presents detailed algorithmic development of statistical models from scratch
* Includes practical applications with over 50 data sets
Key features:
* Integrates R basics with statistical concepts
* Provides graphical presentations inclusive of mathematical expressions
* Aids understanding of limit theorems of probability with and without the simulation approach
* Presents detailed algorithmic development of statistical models from scratch
* Includes practical applications with over 50 data sets
Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models.
Key features:
* Integrates R basics with statistical concepts
* Provides graphical presentations inclusive of mathematical expressions
* Aids understanding of limit theorems of probability with and without the simulation approach
* Presents detailed algorithmic development of statistical models from scratch
* Includes practical applications with over 50 data sets
Key features:
* Integrates R basics with statistical concepts
* Provides graphical presentations inclusive of mathematical expressions
* Aids understanding of limit theorems of probability with and without the simulation approach
* Presents detailed algorithmic development of statistical models from scratch
* Includes practical applications with over 50 data sets
Über den Autor
Prabhanjan Tattar, Business Analysis Senior Advisor at Dell International Services, Bangalore, India. Professor Tattar is a statistician providing analytical solutions to business problems inclusive of statistical models and machine learning as appropriate.
Suresh Ramaiah, Assistant Professor of Statistics at Dharwad University, Dharwad, India.
B G Manjunath, Business Analysis Advisor at Dell International Services, Bangalore, India
Inhaltsverzeichnis
List of Figures xvii
List of Tables xxi
Preface xxiii
Acknowledgments xxv
Part I THE PRELIMINARIES
1 WhyR? 3
1.1 Why R? 3
1.2 R Installation 5
1.3 There is Nothing such as PRACTICALS 5
1.4 Datasets in R and Internet 6
1.4.1 List of Web-sites containing DATASETS 7
1.4.2 Antique Datasets 8
1.5 [...] 9
1.5.1 [...] 10
1.5.2 [...] 10
1.5.3 Is subscribing to R-Mailing List useful? 10
1.6 R and its Interface with other Software 11
1.7 help and/or? 11
1.8 R Books 12
1.9 A Road Map 13
2 The R Basics 15
2.1 Introduction 15
2.2 Simple Arithmetics and a Little Beyond 16
2.2.1 Absolute Values, Remainders, etc. 16
2.2.2 round, floor, etc. 17
2.2.3 Summary Functions 18
2.2.4 Trigonometric Functions 18
2.2.5 Complex Numbers 19
2.2.6 Special Mathematical Functions 21
2.3 Some Basic R Functions 22
2.3.1 Summary Statistics 23
2.3.2 is, as, is.na, etc. 25
2.3.3 factors, levels, etc. 26
2.3.4 Control Programming 27
2.3.5 Other Useful Functions 29
2.3.6 Calculus* 31
2.4 Vectors and Matrices in R 33
2.4.1 Vectors 33
2.4.2 Matrices 36
2.5 Data Entering and Reading from Files 41
2.5.1 Data Entering 41
2.5.2 Reading Data from External Files 43
2.6 Working with Packages 44
2.7 R Session Management 45
2.8 Further Reading 46
2.9 Complements, Problems, and Programs 46
3 Data Preparation and Other Tricks 49
3.1 Introduction 49
3.2 Manipulation with Complex Format Files 50
3.3 Reading Datasets of Foreign Formats 55
3.4 Displaying R Objects 56
3.5 Manipulation Using R Functions 57
3.6 Working with Time and Date 59
3.7 Text Manipulations 62
3.8 Scripts and Text Editors for R 64
3.8.1 Text Editors for Linuxians 64
3.9 Further Reading 65
3.10 Complements, Problems, and Programs 65
4 Exploratory Data Analysis 67
4.1 Introduction: The Tukey's School of Statistics 67
4.2 Essential Summaries of EDA 68
4.3 Graphical Techniques in EDA 71
4.3.1 Boxplot 71
4.3.2 Histogram 76
4.3.3 Histogram Extensions and the Rootogram 79
4.3.4 Pareto Chart 81
4.3.5 Stem-and-Leaf Plot 84
4.3.6 Run Chart 88
4.3.7 Scatter Plot 89
4.4 Quantitative Techniques in EDA 91
4.4.1 Trimean 91
4.4.2 Letter Values 92
4.5 Exploratory Regression Models 95
4.5.1 Resistant Line 95
4.5.2 Median Polish 98
4.6 Further Reading 99
4.7 Complements, Problems, and Programs 100
Part II PROBABILITY AND INFERENCE
5 Probability Theory 105
5.1 Introduction 105
5.2 Sample Space, Set Algebra, and Elementary Probability 106
5.3 Counting Methods 113
5.3.1 Sampling: The Diverse Ways 114
5.3.2 The Binomial Coefficients and the Pascals Triangle 118
5.3.3 Some Problems Based on Combinatorics 119
5.4 Probability: A Definition 122
5.4.1 The Prerequisites 122
5.4.2 The Kolmogorov Definition 127
5.5 Conditional Probability and Independence 130
5.6 Bayes Formula 132
5.7 Random Variables, Expectations, and Moments 133
5.7.1 The Definition 133
5.7.2 Expectation of Random Variables 136
5.8 Distribution Function, Characteristic Function, and Moment Generation Function 143
5.9 Inequalities 145
5.9.1 The Markov Inequality 145
5.9.2 The Jensen's Inequality 145
5.9.3 The Chebyshev Inequality 146
5.10 Convergence of Random Variables 146
5.10.1 Convergence in Distributions 147
5.10.2 Convergence in Probability 150
5.10.3 Convergence in rth Mean 150
5.10.4 Almost Sure Convergence 151
5.11 The Law of Large Numbers 152
5.11.1 The Weak Law of Large Numbers 152
5.12 The Central Limit Theorem 153
5.12.1 The de Moivre-Laplace Central Limit Theorem 153
5.12.2 CLT for iid Case 154
5.12.3 The Lindeberg-Feller CLT 157
5.12.4 The Liapounov CLT 162
5.13 Further Reading 165
5.13.1 Intuitive, Elementary, and First Course Source 165
5.13.2 The Classics and Second Course Source 166
5.13.3 The Problem Books 167
5.13.4 Other Useful Sources 167
5.13.5 R for Probability 167
5.14 Complements, Problems, and Programs 167
6 Probability and Sampling Distributions 171
6.1 Introduction 171
6.2 Discrete Univariate Distributions 172
6.2.1 The Discrete Uniform Distribution 172
6.2.2 The Binomial Distribution 173
6.2.3 The Geometric Distribution 176
6.2.4 The Negative Binomial Distribution 178
6.2.5 Poisson Distribution 179
6.2.6 The Hypergeometric Distribution 182
6.3 Continuous Univariate Distributions 184
6.3.1 The Uniform Distribution 184
6.3.2 The Beta Distribution 186
6.3.3 The Exponential Distribution 187
6.3.4 The Gamma Distribution 188
6.3.5 The Normal Distribution 189
6.3.6 The Cauchy Distribution 191
6.3.7 The t-Distribution 193
6.3.8 The Chi-square Distribution 193
6.3.9 The F-Distribution 194
6.4 Multivariate Probability Distributions 194
6.4.1 The Multinomial Distribution 194
6.4.2 Dirichlet Distribution 195
6.4.3 The Multivariate Normal Distribution 195
6.4.4 The Multivariate t Distribution 196
6.5 Populations and Samples 196
6.6 Sampling from the Normal Distributions 197
6.7 Some Finer Aspects of Sampling Distributions 201
6.7.1 Sampling Distribution of Median 201
6.7.2 Sampling Distribution of Mean of Standard Distributions 201
6.8 Multivariate Sampling Distributions 203
6.8.1 Noncentral Univariate Chi-square, t, and F Distributions 203
6.8.2 Wishart Distribution 205
6.8.3 Hotellings T2 Distribution 206
6.9 Bayesian Sampling Distributions 206
6.10 Further Reading 207
6.11 Complements, Problems, and Programs 208
7 Parametric Inference 209
7.1 Introduction 209
7.2 Families of Distribution 210
7.2.1 The Exponential Family 212
7.2.2 Pitman Family 213
7.3 Loss Functions 214
7.4 Data Reduction 216
7.4.1 Sufficiency 217
7.4.2 Minimal Sufficiency 219
7.5 Likelihood and Information 220
7.5.1 The Likelihood Principle 220
7.5.2 The Fisher Information 226
7.6 Point Estimation 231
7.6.1 Maximum Likelihood Estimation 231
7.6.2 Method of Moments Estimator 239
7.7 Comparison of Estimators 241
7.7.1 Unbiased Estimators 241
7.7.2 Improving Unbiased Estimators 243
7.8 Confidence Intervals 245
7.9 Testing Statistical Hypotheses-The Preliminaries 246
7.10 The Neyman-Pearson Lemma 251
7.11 Uniformly Most Powerful Tests 256
7.12 Uniformly Most Powerful Unbiased Tests 260
7.12.1 Tests for the Means: One- and Two-Sample t-Test 263
7.13 Likelihood Ratio Tests 265
7.13.1 Normal Distribution: One-Sample Problems 266
7.13.2 Normal Distribution: Two-Sample Problem for the Mean 269
7.14 Behrens-Fisher Problem 270
7.15 Multiple Comparison Tests 271
7.15.1 Bonferroni's Method 272
7.15.2 Holm's Method 273
7.16 The EM Algorithm* 274
7.16.1 Introduction 274
7.16.2 The Algorithm 274
7.16.3 Introductory Applications 275
7.17 Further Reading 280
7.17.1 Early Classics 280
7.17.2 Texts from the Last 30 Years 281
7.18 Complements, Problems, and Programs 281
8 Nonparametric Inference 283
8.1 Introduction 283
8.2 Empirical Distribution Function and Its Applications 283
8.2.1 Statistical Functionals 285
8.3 The Jackknife and Bootstrap Methods 288
8.3.1 The Jackknife 288
8.3.2 The Bootstrap 289
8.3.3 Bootstrapping Simple Linear Model* 292
8.4 Non-parametric Smoothing 294
8.4.1 Histogram Smoothing 294
8.4.2 Kernel Smoothing 297
8.4.3 Nonparametric Regression Models* 300
8.5 Non-parametric Tests 304
8.5.1 The Wilcoxon Signed-Ranks Test 305
8.5.2 The Mann-Whitney test 308
8.5.3 The Siegel-Tukey Test 309
8.5.4 The Wald-Wolfowitz Run Test 311
8.5.5 The Kolmogorov-Smirnov Test 312
8.5.6 Kruskal-Wallis Test* 314
8.6 Further Reading 315
8.7 Complements, Problems, and Programs 316
9 Bayesian Inference 317
9.1 Introduction 317
9.2 Bayesian Probabilities 317
9.3 The Bayesian Paradigm for Statistical Inference 321
9.3.1 Bayesian Sufficiency and the Principle 321
9.3.2 Bayesian Analysis and Likelihood Principle 322
9.3.3 Informative and Conjugate Prior 322
9.3.4 Non-informative Prior 323
9.4 Bayesian Estimation 323
9.4.1 Inference for Binomial Distribution 323
9.4.2 Inference for the Poisson Distribution 326
9.4.3 Inference for Uniform Distribution 327
9.4.4 Inference for Exponential Distribution 328
9.4.5 Inference for Normal Distributions 329
9.5 The Credible Intervals 332
9.6 Bayes Factors for Testing Problems 333
9.7 Further Reading 334
9.8 Complements, Problems, and Programs 335
Part III STOCHASTIC PROCESSES AND MONTE CARLO
10 Stochastic Processes 339
10.1 Introduction 339
10.2 Kolmogorov's Consistency Theorem 340
10.3 Markov Chains 341
10.3.1 The m-Step TPM 344
10.3.2 Classification of States 345
10.3.3 Canonical Decomposition of an Absorbing Markov Chain 347
10.3.4 Stationary Distribution and Mean First Passage Time of an Ergodic Markov Chain 350
10.3.5 Time Reversible Markov Chain 352
10.4 Application of Markov Chains in Computational Statistics 352
10.4.1 The Metropolis-Hastings Algorithm 353
10.4.2 Gibbs Sampler 354
10.4.3 Illustrative Examples 355
10.5 Further Reading 361
10.6 Complements, Problems, and Programs 361
11 Monte Carlo Computations 363
11.1 Introduction 363
11.2 Generating the (Pseudo-) Random Numbers 364
11.2.1 Useful Random Generators 364
11.2.2 Probability Through Simulation 366
11.3 Simulation from Probability Distributions and Some Limit Theorems 373
11.3.1 Simulation from Discrete Distributions 373
11.3.2 Simulation from Continuous Distributions 380
11.3.3 Understanding Limit Theorems through Simulation 383
11.3.4 Understanding The Central Limit Theorem 386
11.4 Monte Carlo Integration 388
11.5 The Accept-Reject Technique 390
11.6 Application to Bayesian Inference 394
11.7 Further Reading 397
11.8 Complements, Problems, and Programs 397
Part IV LINEAR MODELS
12 Linear Regression Models 401
12.1 Introduction 401
12.2 Simple Linear Regression Model 402
12.2.1 Fitting a Linear Model 403
12.2.2 Confidence Intervals 405
12.2.3 The Analysis of Variance (ANOVA) 407
12.2.4 The Coefficient of Determination 409
12.2.5 The "lm" Function from R 410
12.2.6 Residuals for Validation of the Model Assumptions 412
12.2.7 Prediction for the Simple Regression Model 416
12.2.8 Regression through the Origin...
List of Tables xxi
Preface xxiii
Acknowledgments xxv
Part I THE PRELIMINARIES
1 WhyR? 3
1.1 Why R? 3
1.2 R Installation 5
1.3 There is Nothing such as PRACTICALS 5
1.4 Datasets in R and Internet 6
1.4.1 List of Web-sites containing DATASETS 7
1.4.2 Antique Datasets 8
1.5 [...] 9
1.5.1 [...] 10
1.5.2 [...] 10
1.5.3 Is subscribing to R-Mailing List useful? 10
1.6 R and its Interface with other Software 11
1.7 help and/or? 11
1.8 R Books 12
1.9 A Road Map 13
2 The R Basics 15
2.1 Introduction 15
2.2 Simple Arithmetics and a Little Beyond 16
2.2.1 Absolute Values, Remainders, etc. 16
2.2.2 round, floor, etc. 17
2.2.3 Summary Functions 18
2.2.4 Trigonometric Functions 18
2.2.5 Complex Numbers 19
2.2.6 Special Mathematical Functions 21
2.3 Some Basic R Functions 22
2.3.1 Summary Statistics 23
2.3.2 is, as, is.na, etc. 25
2.3.3 factors, levels, etc. 26
2.3.4 Control Programming 27
2.3.5 Other Useful Functions 29
2.3.6 Calculus* 31
2.4 Vectors and Matrices in R 33
2.4.1 Vectors 33
2.4.2 Matrices 36
2.5 Data Entering and Reading from Files 41
2.5.1 Data Entering 41
2.5.2 Reading Data from External Files 43
2.6 Working with Packages 44
2.7 R Session Management 45
2.8 Further Reading 46
2.9 Complements, Problems, and Programs 46
3 Data Preparation and Other Tricks 49
3.1 Introduction 49
3.2 Manipulation with Complex Format Files 50
3.3 Reading Datasets of Foreign Formats 55
3.4 Displaying R Objects 56
3.5 Manipulation Using R Functions 57
3.6 Working with Time and Date 59
3.7 Text Manipulations 62
3.8 Scripts and Text Editors for R 64
3.8.1 Text Editors for Linuxians 64
3.9 Further Reading 65
3.10 Complements, Problems, and Programs 65
4 Exploratory Data Analysis 67
4.1 Introduction: The Tukey's School of Statistics 67
4.2 Essential Summaries of EDA 68
4.3 Graphical Techniques in EDA 71
4.3.1 Boxplot 71
4.3.2 Histogram 76
4.3.3 Histogram Extensions and the Rootogram 79
4.3.4 Pareto Chart 81
4.3.5 Stem-and-Leaf Plot 84
4.3.6 Run Chart 88
4.3.7 Scatter Plot 89
4.4 Quantitative Techniques in EDA 91
4.4.1 Trimean 91
4.4.2 Letter Values 92
4.5 Exploratory Regression Models 95
4.5.1 Resistant Line 95
4.5.2 Median Polish 98
4.6 Further Reading 99
4.7 Complements, Problems, and Programs 100
Part II PROBABILITY AND INFERENCE
5 Probability Theory 105
5.1 Introduction 105
5.2 Sample Space, Set Algebra, and Elementary Probability 106
5.3 Counting Methods 113
5.3.1 Sampling: The Diverse Ways 114
5.3.2 The Binomial Coefficients and the Pascals Triangle 118
5.3.3 Some Problems Based on Combinatorics 119
5.4 Probability: A Definition 122
5.4.1 The Prerequisites 122
5.4.2 The Kolmogorov Definition 127
5.5 Conditional Probability and Independence 130
5.6 Bayes Formula 132
5.7 Random Variables, Expectations, and Moments 133
5.7.1 The Definition 133
5.7.2 Expectation of Random Variables 136
5.8 Distribution Function, Characteristic Function, and Moment Generation Function 143
5.9 Inequalities 145
5.9.1 The Markov Inequality 145
5.9.2 The Jensen's Inequality 145
5.9.3 The Chebyshev Inequality 146
5.10 Convergence of Random Variables 146
5.10.1 Convergence in Distributions 147
5.10.2 Convergence in Probability 150
5.10.3 Convergence in rth Mean 150
5.10.4 Almost Sure Convergence 151
5.11 The Law of Large Numbers 152
5.11.1 The Weak Law of Large Numbers 152
5.12 The Central Limit Theorem 153
5.12.1 The de Moivre-Laplace Central Limit Theorem 153
5.12.2 CLT for iid Case 154
5.12.3 The Lindeberg-Feller CLT 157
5.12.4 The Liapounov CLT 162
5.13 Further Reading 165
5.13.1 Intuitive, Elementary, and First Course Source 165
5.13.2 The Classics and Second Course Source 166
5.13.3 The Problem Books 167
5.13.4 Other Useful Sources 167
5.13.5 R for Probability 167
5.14 Complements, Problems, and Programs 167
6 Probability and Sampling Distributions 171
6.1 Introduction 171
6.2 Discrete Univariate Distributions 172
6.2.1 The Discrete Uniform Distribution 172
6.2.2 The Binomial Distribution 173
6.2.3 The Geometric Distribution 176
6.2.4 The Negative Binomial Distribution 178
6.2.5 Poisson Distribution 179
6.2.6 The Hypergeometric Distribution 182
6.3 Continuous Univariate Distributions 184
6.3.1 The Uniform Distribution 184
6.3.2 The Beta Distribution 186
6.3.3 The Exponential Distribution 187
6.3.4 The Gamma Distribution 188
6.3.5 The Normal Distribution 189
6.3.6 The Cauchy Distribution 191
6.3.7 The t-Distribution 193
6.3.8 The Chi-square Distribution 193
6.3.9 The F-Distribution 194
6.4 Multivariate Probability Distributions 194
6.4.1 The Multinomial Distribution 194
6.4.2 Dirichlet Distribution 195
6.4.3 The Multivariate Normal Distribution 195
6.4.4 The Multivariate t Distribution 196
6.5 Populations and Samples 196
6.6 Sampling from the Normal Distributions 197
6.7 Some Finer Aspects of Sampling Distributions 201
6.7.1 Sampling Distribution of Median 201
6.7.2 Sampling Distribution of Mean of Standard Distributions 201
6.8 Multivariate Sampling Distributions 203
6.8.1 Noncentral Univariate Chi-square, t, and F Distributions 203
6.8.2 Wishart Distribution 205
6.8.3 Hotellings T2 Distribution 206
6.9 Bayesian Sampling Distributions 206
6.10 Further Reading 207
6.11 Complements, Problems, and Programs 208
7 Parametric Inference 209
7.1 Introduction 209
7.2 Families of Distribution 210
7.2.1 The Exponential Family 212
7.2.2 Pitman Family 213
7.3 Loss Functions 214
7.4 Data Reduction 216
7.4.1 Sufficiency 217
7.4.2 Minimal Sufficiency 219
7.5 Likelihood and Information 220
7.5.1 The Likelihood Principle 220
7.5.2 The Fisher Information 226
7.6 Point Estimation 231
7.6.1 Maximum Likelihood Estimation 231
7.6.2 Method of Moments Estimator 239
7.7 Comparison of Estimators 241
7.7.1 Unbiased Estimators 241
7.7.2 Improving Unbiased Estimators 243
7.8 Confidence Intervals 245
7.9 Testing Statistical Hypotheses-The Preliminaries 246
7.10 The Neyman-Pearson Lemma 251
7.11 Uniformly Most Powerful Tests 256
7.12 Uniformly Most Powerful Unbiased Tests 260
7.12.1 Tests for the Means: One- and Two-Sample t-Test 263
7.13 Likelihood Ratio Tests 265
7.13.1 Normal Distribution: One-Sample Problems 266
7.13.2 Normal Distribution: Two-Sample Problem for the Mean 269
7.14 Behrens-Fisher Problem 270
7.15 Multiple Comparison Tests 271
7.15.1 Bonferroni's Method 272
7.15.2 Holm's Method 273
7.16 The EM Algorithm* 274
7.16.1 Introduction 274
7.16.2 The Algorithm 274
7.16.3 Introductory Applications 275
7.17 Further Reading 280
7.17.1 Early Classics 280
7.17.2 Texts from the Last 30 Years 281
7.18 Complements, Problems, and Programs 281
8 Nonparametric Inference 283
8.1 Introduction 283
8.2 Empirical Distribution Function and Its Applications 283
8.2.1 Statistical Functionals 285
8.3 The Jackknife and Bootstrap Methods 288
8.3.1 The Jackknife 288
8.3.2 The Bootstrap 289
8.3.3 Bootstrapping Simple Linear Model* 292
8.4 Non-parametric Smoothing 294
8.4.1 Histogram Smoothing 294
8.4.2 Kernel Smoothing 297
8.4.3 Nonparametric Regression Models* 300
8.5 Non-parametric Tests 304
8.5.1 The Wilcoxon Signed-Ranks Test 305
8.5.2 The Mann-Whitney test 308
8.5.3 The Siegel-Tukey Test 309
8.5.4 The Wald-Wolfowitz Run Test 311
8.5.5 The Kolmogorov-Smirnov Test 312
8.5.6 Kruskal-Wallis Test* 314
8.6 Further Reading 315
8.7 Complements, Problems, and Programs 316
9 Bayesian Inference 317
9.1 Introduction 317
9.2 Bayesian Probabilities 317
9.3 The Bayesian Paradigm for Statistical Inference 321
9.3.1 Bayesian Sufficiency and the Principle 321
9.3.2 Bayesian Analysis and Likelihood Principle 322
9.3.3 Informative and Conjugate Prior 322
9.3.4 Non-informative Prior 323
9.4 Bayesian Estimation 323
9.4.1 Inference for Binomial Distribution 323
9.4.2 Inference for the Poisson Distribution 326
9.4.3 Inference for Uniform Distribution 327
9.4.4 Inference for Exponential Distribution 328
9.4.5 Inference for Normal Distributions 329
9.5 The Credible Intervals 332
9.6 Bayes Factors for Testing Problems 333
9.7 Further Reading 334
9.8 Complements, Problems, and Programs 335
Part III STOCHASTIC PROCESSES AND MONTE CARLO
10 Stochastic Processes 339
10.1 Introduction 339
10.2 Kolmogorov's Consistency Theorem 340
10.3 Markov Chains 341
10.3.1 The m-Step TPM 344
10.3.2 Classification of States 345
10.3.3 Canonical Decomposition of an Absorbing Markov Chain 347
10.3.4 Stationary Distribution and Mean First Passage Time of an Ergodic Markov Chain 350
10.3.5 Time Reversible Markov Chain 352
10.4 Application of Markov Chains in Computational Statistics 352
10.4.1 The Metropolis-Hastings Algorithm 353
10.4.2 Gibbs Sampler 354
10.4.3 Illustrative Examples 355
10.5 Further Reading 361
10.6 Complements, Problems, and Programs 361
11 Monte Carlo Computations 363
11.1 Introduction 363
11.2 Generating the (Pseudo-) Random Numbers 364
11.2.1 Useful Random Generators 364
11.2.2 Probability Through Simulation 366
11.3 Simulation from Probability Distributions and Some Limit Theorems 373
11.3.1 Simulation from Discrete Distributions 373
11.3.2 Simulation from Continuous Distributions 380
11.3.3 Understanding Limit Theorems through Simulation 383
11.3.4 Understanding The Central Limit Theorem 386
11.4 Monte Carlo Integration 388
11.5 The Accept-Reject Technique 390
11.6 Application to Bayesian Inference 394
11.7 Further Reading 397
11.8 Complements, Problems, and Programs 397
Part IV LINEAR MODELS
12 Linear Regression Models 401
12.1 Introduction 401
12.2 Simple Linear Regression Model 402
12.2.1 Fitting a Linear Model 403
12.2.2 Confidence Intervals 405
12.2.3 The Analysis of Variance (ANOVA) 407
12.2.4 The Coefficient of Determination 409
12.2.5 The "lm" Function from R 410
12.2.6 Residuals for Validation of the Model Assumptions 412
12.2.7 Prediction for the Simple Regression Model 416
12.2.8 Regression through the Origin...
Details
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 696 |
| Inhalt: | 692 S. |
| ISBN-13: | 9781119152729 |
| ISBN-10: | 1119152720 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: |
Tattar, Prabhanjan N
Ramaiah, Suresh Manjunath, B G |
| Hersteller: |
Wiley
John Wiley & Sons |
| Maße: | 250 x 175 x 41 mm |
| Von/Mit: | Prabhanjan N Tattar (u. a.) |
| Erscheinungsdatum: | 02.05.2016 |
| Gewicht: | 1,355 kg |
Über den Autor
Prabhanjan Tattar, Business Analysis Senior Advisor at Dell International Services, Bangalore, India. Professor Tattar is a statistician providing analytical solutions to business problems inclusive of statistical models and machine learning as appropriate.
Suresh Ramaiah, Assistant Professor of Statistics at Dharwad University, Dharwad, India.
B G Manjunath, Business Analysis Advisor at Dell International Services, Bangalore, India
Inhaltsverzeichnis
List of Figures xvii
List of Tables xxi
Preface xxiii
Acknowledgments xxv
Part I THE PRELIMINARIES
1 WhyR? 3
1.1 Why R? 3
1.2 R Installation 5
1.3 There is Nothing such as PRACTICALS 5
1.4 Datasets in R and Internet 6
1.4.1 List of Web-sites containing DATASETS 7
1.4.2 Antique Datasets 8
1.5 [...] 9
1.5.1 [...] 10
1.5.2 [...] 10
1.5.3 Is subscribing to R-Mailing List useful? 10
1.6 R and its Interface with other Software 11
1.7 help and/or? 11
1.8 R Books 12
1.9 A Road Map 13
2 The R Basics 15
2.1 Introduction 15
2.2 Simple Arithmetics and a Little Beyond 16
2.2.1 Absolute Values, Remainders, etc. 16
2.2.2 round, floor, etc. 17
2.2.3 Summary Functions 18
2.2.4 Trigonometric Functions 18
2.2.5 Complex Numbers 19
2.2.6 Special Mathematical Functions 21
2.3 Some Basic R Functions 22
2.3.1 Summary Statistics 23
2.3.2 is, as, is.na, etc. 25
2.3.3 factors, levels, etc. 26
2.3.4 Control Programming 27
2.3.5 Other Useful Functions 29
2.3.6 Calculus* 31
2.4 Vectors and Matrices in R 33
2.4.1 Vectors 33
2.4.2 Matrices 36
2.5 Data Entering and Reading from Files 41
2.5.1 Data Entering 41
2.5.2 Reading Data from External Files 43
2.6 Working with Packages 44
2.7 R Session Management 45
2.8 Further Reading 46
2.9 Complements, Problems, and Programs 46
3 Data Preparation and Other Tricks 49
3.1 Introduction 49
3.2 Manipulation with Complex Format Files 50
3.3 Reading Datasets of Foreign Formats 55
3.4 Displaying R Objects 56
3.5 Manipulation Using R Functions 57
3.6 Working with Time and Date 59
3.7 Text Manipulations 62
3.8 Scripts and Text Editors for R 64
3.8.1 Text Editors for Linuxians 64
3.9 Further Reading 65
3.10 Complements, Problems, and Programs 65
4 Exploratory Data Analysis 67
4.1 Introduction: The Tukey's School of Statistics 67
4.2 Essential Summaries of EDA 68
4.3 Graphical Techniques in EDA 71
4.3.1 Boxplot 71
4.3.2 Histogram 76
4.3.3 Histogram Extensions and the Rootogram 79
4.3.4 Pareto Chart 81
4.3.5 Stem-and-Leaf Plot 84
4.3.6 Run Chart 88
4.3.7 Scatter Plot 89
4.4 Quantitative Techniques in EDA 91
4.4.1 Trimean 91
4.4.2 Letter Values 92
4.5 Exploratory Regression Models 95
4.5.1 Resistant Line 95
4.5.2 Median Polish 98
4.6 Further Reading 99
4.7 Complements, Problems, and Programs 100
Part II PROBABILITY AND INFERENCE
5 Probability Theory 105
5.1 Introduction 105
5.2 Sample Space, Set Algebra, and Elementary Probability 106
5.3 Counting Methods 113
5.3.1 Sampling: The Diverse Ways 114
5.3.2 The Binomial Coefficients and the Pascals Triangle 118
5.3.3 Some Problems Based on Combinatorics 119
5.4 Probability: A Definition 122
5.4.1 The Prerequisites 122
5.4.2 The Kolmogorov Definition 127
5.5 Conditional Probability and Independence 130
5.6 Bayes Formula 132
5.7 Random Variables, Expectations, and Moments 133
5.7.1 The Definition 133
5.7.2 Expectation of Random Variables 136
5.8 Distribution Function, Characteristic Function, and Moment Generation Function 143
5.9 Inequalities 145
5.9.1 The Markov Inequality 145
5.9.2 The Jensen's Inequality 145
5.9.3 The Chebyshev Inequality 146
5.10 Convergence of Random Variables 146
5.10.1 Convergence in Distributions 147
5.10.2 Convergence in Probability 150
5.10.3 Convergence in rth Mean 150
5.10.4 Almost Sure Convergence 151
5.11 The Law of Large Numbers 152
5.11.1 The Weak Law of Large Numbers 152
5.12 The Central Limit Theorem 153
5.12.1 The de Moivre-Laplace Central Limit Theorem 153
5.12.2 CLT for iid Case 154
5.12.3 The Lindeberg-Feller CLT 157
5.12.4 The Liapounov CLT 162
5.13 Further Reading 165
5.13.1 Intuitive, Elementary, and First Course Source 165
5.13.2 The Classics and Second Course Source 166
5.13.3 The Problem Books 167
5.13.4 Other Useful Sources 167
5.13.5 R for Probability 167
5.14 Complements, Problems, and Programs 167
6 Probability and Sampling Distributions 171
6.1 Introduction 171
6.2 Discrete Univariate Distributions 172
6.2.1 The Discrete Uniform Distribution 172
6.2.2 The Binomial Distribution 173
6.2.3 The Geometric Distribution 176
6.2.4 The Negative Binomial Distribution 178
6.2.5 Poisson Distribution 179
6.2.6 The Hypergeometric Distribution 182
6.3 Continuous Univariate Distributions 184
6.3.1 The Uniform Distribution 184
6.3.2 The Beta Distribution 186
6.3.3 The Exponential Distribution 187
6.3.4 The Gamma Distribution 188
6.3.5 The Normal Distribution 189
6.3.6 The Cauchy Distribution 191
6.3.7 The t-Distribution 193
6.3.8 The Chi-square Distribution 193
6.3.9 The F-Distribution 194
6.4 Multivariate Probability Distributions 194
6.4.1 The Multinomial Distribution 194
6.4.2 Dirichlet Distribution 195
6.4.3 The Multivariate Normal Distribution 195
6.4.4 The Multivariate t Distribution 196
6.5 Populations and Samples 196
6.6 Sampling from the Normal Distributions 197
6.7 Some Finer Aspects of Sampling Distributions 201
6.7.1 Sampling Distribution of Median 201
6.7.2 Sampling Distribution of Mean of Standard Distributions 201
6.8 Multivariate Sampling Distributions 203
6.8.1 Noncentral Univariate Chi-square, t, and F Distributions 203
6.8.2 Wishart Distribution 205
6.8.3 Hotellings T2 Distribution 206
6.9 Bayesian Sampling Distributions 206
6.10 Further Reading 207
6.11 Complements, Problems, and Programs 208
7 Parametric Inference 209
7.1 Introduction 209
7.2 Families of Distribution 210
7.2.1 The Exponential Family 212
7.2.2 Pitman Family 213
7.3 Loss Functions 214
7.4 Data Reduction 216
7.4.1 Sufficiency 217
7.4.2 Minimal Sufficiency 219
7.5 Likelihood and Information 220
7.5.1 The Likelihood Principle 220
7.5.2 The Fisher Information 226
7.6 Point Estimation 231
7.6.1 Maximum Likelihood Estimation 231
7.6.2 Method of Moments Estimator 239
7.7 Comparison of Estimators 241
7.7.1 Unbiased Estimators 241
7.7.2 Improving Unbiased Estimators 243
7.8 Confidence Intervals 245
7.9 Testing Statistical Hypotheses-The Preliminaries 246
7.10 The Neyman-Pearson Lemma 251
7.11 Uniformly Most Powerful Tests 256
7.12 Uniformly Most Powerful Unbiased Tests 260
7.12.1 Tests for the Means: One- and Two-Sample t-Test 263
7.13 Likelihood Ratio Tests 265
7.13.1 Normal Distribution: One-Sample Problems 266
7.13.2 Normal Distribution: Two-Sample Problem for the Mean 269
7.14 Behrens-Fisher Problem 270
7.15 Multiple Comparison Tests 271
7.15.1 Bonferroni's Method 272
7.15.2 Holm's Method 273
7.16 The EM Algorithm* 274
7.16.1 Introduction 274
7.16.2 The Algorithm 274
7.16.3 Introductory Applications 275
7.17 Further Reading 280
7.17.1 Early Classics 280
7.17.2 Texts from the Last 30 Years 281
7.18 Complements, Problems, and Programs 281
8 Nonparametric Inference 283
8.1 Introduction 283
8.2 Empirical Distribution Function and Its Applications 283
8.2.1 Statistical Functionals 285
8.3 The Jackknife and Bootstrap Methods 288
8.3.1 The Jackknife 288
8.3.2 The Bootstrap 289
8.3.3 Bootstrapping Simple Linear Model* 292
8.4 Non-parametric Smoothing 294
8.4.1 Histogram Smoothing 294
8.4.2 Kernel Smoothing 297
8.4.3 Nonparametric Regression Models* 300
8.5 Non-parametric Tests 304
8.5.1 The Wilcoxon Signed-Ranks Test 305
8.5.2 The Mann-Whitney test 308
8.5.3 The Siegel-Tukey Test 309
8.5.4 The Wald-Wolfowitz Run Test 311
8.5.5 The Kolmogorov-Smirnov Test 312
8.5.6 Kruskal-Wallis Test* 314
8.6 Further Reading 315
8.7 Complements, Problems, and Programs 316
9 Bayesian Inference 317
9.1 Introduction 317
9.2 Bayesian Probabilities 317
9.3 The Bayesian Paradigm for Statistical Inference 321
9.3.1 Bayesian Sufficiency and the Principle 321
9.3.2 Bayesian Analysis and Likelihood Principle 322
9.3.3 Informative and Conjugate Prior 322
9.3.4 Non-informative Prior 323
9.4 Bayesian Estimation 323
9.4.1 Inference for Binomial Distribution 323
9.4.2 Inference for the Poisson Distribution 326
9.4.3 Inference for Uniform Distribution 327
9.4.4 Inference for Exponential Distribution 328
9.4.5 Inference for Normal Distributions 329
9.5 The Credible Intervals 332
9.6 Bayes Factors for Testing Problems 333
9.7 Further Reading 334
9.8 Complements, Problems, and Programs 335
Part III STOCHASTIC PROCESSES AND MONTE CARLO
10 Stochastic Processes 339
10.1 Introduction 339
10.2 Kolmogorov's Consistency Theorem 340
10.3 Markov Chains 341
10.3.1 The m-Step TPM 344
10.3.2 Classification of States 345
10.3.3 Canonical Decomposition of an Absorbing Markov Chain 347
10.3.4 Stationary Distribution and Mean First Passage Time of an Ergodic Markov Chain 350
10.3.5 Time Reversible Markov Chain 352
10.4 Application of Markov Chains in Computational Statistics 352
10.4.1 The Metropolis-Hastings Algorithm 353
10.4.2 Gibbs Sampler 354
10.4.3 Illustrative Examples 355
10.5 Further Reading 361
10.6 Complements, Problems, and Programs 361
11 Monte Carlo Computations 363
11.1 Introduction 363
11.2 Generating the (Pseudo-) Random Numbers 364
11.2.1 Useful Random Generators 364
11.2.2 Probability Through Simulation 366
11.3 Simulation from Probability Distributions and Some Limit Theorems 373
11.3.1 Simulation from Discrete Distributions 373
11.3.2 Simulation from Continuous Distributions 380
11.3.3 Understanding Limit Theorems through Simulation 383
11.3.4 Understanding The Central Limit Theorem 386
11.4 Monte Carlo Integration 388
11.5 The Accept-Reject Technique 390
11.6 Application to Bayesian Inference 394
11.7 Further Reading 397
11.8 Complements, Problems, and Programs 397
Part IV LINEAR MODELS
12 Linear Regression Models 401
12.1 Introduction 401
12.2 Simple Linear Regression Model 402
12.2.1 Fitting a Linear Model 403
12.2.2 Confidence Intervals 405
12.2.3 The Analysis of Variance (ANOVA) 407
12.2.4 The Coefficient of Determination 409
12.2.5 The "lm" Function from R 410
12.2.6 Residuals for Validation of the Model Assumptions 412
12.2.7 Prediction for the Simple Regression Model 416
12.2.8 Regression through the Origin...
List of Tables xxi
Preface xxiii
Acknowledgments xxv
Part I THE PRELIMINARIES
1 WhyR? 3
1.1 Why R? 3
1.2 R Installation 5
1.3 There is Nothing such as PRACTICALS 5
1.4 Datasets in R and Internet 6
1.4.1 List of Web-sites containing DATASETS 7
1.4.2 Antique Datasets 8
1.5 [...] 9
1.5.1 [...] 10
1.5.2 [...] 10
1.5.3 Is subscribing to R-Mailing List useful? 10
1.6 R and its Interface with other Software 11
1.7 help and/or? 11
1.8 R Books 12
1.9 A Road Map 13
2 The R Basics 15
2.1 Introduction 15
2.2 Simple Arithmetics and a Little Beyond 16
2.2.1 Absolute Values, Remainders, etc. 16
2.2.2 round, floor, etc. 17
2.2.3 Summary Functions 18
2.2.4 Trigonometric Functions 18
2.2.5 Complex Numbers 19
2.2.6 Special Mathematical Functions 21
2.3 Some Basic R Functions 22
2.3.1 Summary Statistics 23
2.3.2 is, as, is.na, etc. 25
2.3.3 factors, levels, etc. 26
2.3.4 Control Programming 27
2.3.5 Other Useful Functions 29
2.3.6 Calculus* 31
2.4 Vectors and Matrices in R 33
2.4.1 Vectors 33
2.4.2 Matrices 36
2.5 Data Entering and Reading from Files 41
2.5.1 Data Entering 41
2.5.2 Reading Data from External Files 43
2.6 Working with Packages 44
2.7 R Session Management 45
2.8 Further Reading 46
2.9 Complements, Problems, and Programs 46
3 Data Preparation and Other Tricks 49
3.1 Introduction 49
3.2 Manipulation with Complex Format Files 50
3.3 Reading Datasets of Foreign Formats 55
3.4 Displaying R Objects 56
3.5 Manipulation Using R Functions 57
3.6 Working with Time and Date 59
3.7 Text Manipulations 62
3.8 Scripts and Text Editors for R 64
3.8.1 Text Editors for Linuxians 64
3.9 Further Reading 65
3.10 Complements, Problems, and Programs 65
4 Exploratory Data Analysis 67
4.1 Introduction: The Tukey's School of Statistics 67
4.2 Essential Summaries of EDA 68
4.3 Graphical Techniques in EDA 71
4.3.1 Boxplot 71
4.3.2 Histogram 76
4.3.3 Histogram Extensions and the Rootogram 79
4.3.4 Pareto Chart 81
4.3.5 Stem-and-Leaf Plot 84
4.3.6 Run Chart 88
4.3.7 Scatter Plot 89
4.4 Quantitative Techniques in EDA 91
4.4.1 Trimean 91
4.4.2 Letter Values 92
4.5 Exploratory Regression Models 95
4.5.1 Resistant Line 95
4.5.2 Median Polish 98
4.6 Further Reading 99
4.7 Complements, Problems, and Programs 100
Part II PROBABILITY AND INFERENCE
5 Probability Theory 105
5.1 Introduction 105
5.2 Sample Space, Set Algebra, and Elementary Probability 106
5.3 Counting Methods 113
5.3.1 Sampling: The Diverse Ways 114
5.3.2 The Binomial Coefficients and the Pascals Triangle 118
5.3.3 Some Problems Based on Combinatorics 119
5.4 Probability: A Definition 122
5.4.1 The Prerequisites 122
5.4.2 The Kolmogorov Definition 127
5.5 Conditional Probability and Independence 130
5.6 Bayes Formula 132
5.7 Random Variables, Expectations, and Moments 133
5.7.1 The Definition 133
5.7.2 Expectation of Random Variables 136
5.8 Distribution Function, Characteristic Function, and Moment Generation Function 143
5.9 Inequalities 145
5.9.1 The Markov Inequality 145
5.9.2 The Jensen's Inequality 145
5.9.3 The Chebyshev Inequality 146
5.10 Convergence of Random Variables 146
5.10.1 Convergence in Distributions 147
5.10.2 Convergence in Probability 150
5.10.3 Convergence in rth Mean 150
5.10.4 Almost Sure Convergence 151
5.11 The Law of Large Numbers 152
5.11.1 The Weak Law of Large Numbers 152
5.12 The Central Limit Theorem 153
5.12.1 The de Moivre-Laplace Central Limit Theorem 153
5.12.2 CLT for iid Case 154
5.12.3 The Lindeberg-Feller CLT 157
5.12.4 The Liapounov CLT 162
5.13 Further Reading 165
5.13.1 Intuitive, Elementary, and First Course Source 165
5.13.2 The Classics and Second Course Source 166
5.13.3 The Problem Books 167
5.13.4 Other Useful Sources 167
5.13.5 R for Probability 167
5.14 Complements, Problems, and Programs 167
6 Probability and Sampling Distributions 171
6.1 Introduction 171
6.2 Discrete Univariate Distributions 172
6.2.1 The Discrete Uniform Distribution 172
6.2.2 The Binomial Distribution 173
6.2.3 The Geometric Distribution 176
6.2.4 The Negative Binomial Distribution 178
6.2.5 Poisson Distribution 179
6.2.6 The Hypergeometric Distribution 182
6.3 Continuous Univariate Distributions 184
6.3.1 The Uniform Distribution 184
6.3.2 The Beta Distribution 186
6.3.3 The Exponential Distribution 187
6.3.4 The Gamma Distribution 188
6.3.5 The Normal Distribution 189
6.3.6 The Cauchy Distribution 191
6.3.7 The t-Distribution 193
6.3.8 The Chi-square Distribution 193
6.3.9 The F-Distribution 194
6.4 Multivariate Probability Distributions 194
6.4.1 The Multinomial Distribution 194
6.4.2 Dirichlet Distribution 195
6.4.3 The Multivariate Normal Distribution 195
6.4.4 The Multivariate t Distribution 196
6.5 Populations and Samples 196
6.6 Sampling from the Normal Distributions 197
6.7 Some Finer Aspects of Sampling Distributions 201
6.7.1 Sampling Distribution of Median 201
6.7.2 Sampling Distribution of Mean of Standard Distributions 201
6.8 Multivariate Sampling Distributions 203
6.8.1 Noncentral Univariate Chi-square, t, and F Distributions 203
6.8.2 Wishart Distribution 205
6.8.3 Hotellings T2 Distribution 206
6.9 Bayesian Sampling Distributions 206
6.10 Further Reading 207
6.11 Complements, Problems, and Programs 208
7 Parametric Inference 209
7.1 Introduction 209
7.2 Families of Distribution 210
7.2.1 The Exponential Family 212
7.2.2 Pitman Family 213
7.3 Loss Functions 214
7.4 Data Reduction 216
7.4.1 Sufficiency 217
7.4.2 Minimal Sufficiency 219
7.5 Likelihood and Information 220
7.5.1 The Likelihood Principle 220
7.5.2 The Fisher Information 226
7.6 Point Estimation 231
7.6.1 Maximum Likelihood Estimation 231
7.6.2 Method of Moments Estimator 239
7.7 Comparison of Estimators 241
7.7.1 Unbiased Estimators 241
7.7.2 Improving Unbiased Estimators 243
7.8 Confidence Intervals 245
7.9 Testing Statistical Hypotheses-The Preliminaries 246
7.10 The Neyman-Pearson Lemma 251
7.11 Uniformly Most Powerful Tests 256
7.12 Uniformly Most Powerful Unbiased Tests 260
7.12.1 Tests for the Means: One- and Two-Sample t-Test 263
7.13 Likelihood Ratio Tests 265
7.13.1 Normal Distribution: One-Sample Problems 266
7.13.2 Normal Distribution: Two-Sample Problem for the Mean 269
7.14 Behrens-Fisher Problem 270
7.15 Multiple Comparison Tests 271
7.15.1 Bonferroni's Method 272
7.15.2 Holm's Method 273
7.16 The EM Algorithm* 274
7.16.1 Introduction 274
7.16.2 The Algorithm 274
7.16.3 Introductory Applications 275
7.17 Further Reading 280
7.17.1 Early Classics 280
7.17.2 Texts from the Last 30 Years 281
7.18 Complements, Problems, and Programs 281
8 Nonparametric Inference 283
8.1 Introduction 283
8.2 Empirical Distribution Function and Its Applications 283
8.2.1 Statistical Functionals 285
8.3 The Jackknife and Bootstrap Methods 288
8.3.1 The Jackknife 288
8.3.2 The Bootstrap 289
8.3.3 Bootstrapping Simple Linear Model* 292
8.4 Non-parametric Smoothing 294
8.4.1 Histogram Smoothing 294
8.4.2 Kernel Smoothing 297
8.4.3 Nonparametric Regression Models* 300
8.5 Non-parametric Tests 304
8.5.1 The Wilcoxon Signed-Ranks Test 305
8.5.2 The Mann-Whitney test 308
8.5.3 The Siegel-Tukey Test 309
8.5.4 The Wald-Wolfowitz Run Test 311
8.5.5 The Kolmogorov-Smirnov Test 312
8.5.6 Kruskal-Wallis Test* 314
8.6 Further Reading 315
8.7 Complements, Problems, and Programs 316
9 Bayesian Inference 317
9.1 Introduction 317
9.2 Bayesian Probabilities 317
9.3 The Bayesian Paradigm for Statistical Inference 321
9.3.1 Bayesian Sufficiency and the Principle 321
9.3.2 Bayesian Analysis and Likelihood Principle 322
9.3.3 Informative and Conjugate Prior 322
9.3.4 Non-informative Prior 323
9.4 Bayesian Estimation 323
9.4.1 Inference for Binomial Distribution 323
9.4.2 Inference for the Poisson Distribution 326
9.4.3 Inference for Uniform Distribution 327
9.4.4 Inference for Exponential Distribution 328
9.4.5 Inference for Normal Distributions 329
9.5 The Credible Intervals 332
9.6 Bayes Factors for Testing Problems 333
9.7 Further Reading 334
9.8 Complements, Problems, and Programs 335
Part III STOCHASTIC PROCESSES AND MONTE CARLO
10 Stochastic Processes 339
10.1 Introduction 339
10.2 Kolmogorov's Consistency Theorem 340
10.3 Markov Chains 341
10.3.1 The m-Step TPM 344
10.3.2 Classification of States 345
10.3.3 Canonical Decomposition of an Absorbing Markov Chain 347
10.3.4 Stationary Distribution and Mean First Passage Time of an Ergodic Markov Chain 350
10.3.5 Time Reversible Markov Chain 352
10.4 Application of Markov Chains in Computational Statistics 352
10.4.1 The Metropolis-Hastings Algorithm 353
10.4.2 Gibbs Sampler 354
10.4.3 Illustrative Examples 355
10.5 Further Reading 361
10.6 Complements, Problems, and Programs 361
11 Monte Carlo Computations 363
11.1 Introduction 363
11.2 Generating the (Pseudo-) Random Numbers 364
11.2.1 Useful Random Generators 364
11.2.2 Probability Through Simulation 366
11.3 Simulation from Probability Distributions and Some Limit Theorems 373
11.3.1 Simulation from Discrete Distributions 373
11.3.2 Simulation from Continuous Distributions 380
11.3.3 Understanding Limit Theorems through Simulation 383
11.3.4 Understanding The Central Limit Theorem 386
11.4 Monte Carlo Integration 388
11.5 The Accept-Reject Technique 390
11.6 Application to Bayesian Inference 394
11.7 Further Reading 397
11.8 Complements, Problems, and Programs 397
Part IV LINEAR MODELS
12 Linear Regression Models 401
12.1 Introduction 401
12.2 Simple Linear Regression Model 402
12.2.1 Fitting a Linear Model 403
12.2.2 Confidence Intervals 405
12.2.3 The Analysis of Variance (ANOVA) 407
12.2.4 The Coefficient of Determination 409
12.2.5 The "lm" Function from R 410
12.2.6 Residuals for Validation of the Model Assumptions 412
12.2.7 Prediction for the Simple Regression Model 416
12.2.8 Regression through the Origin...
Details
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 696 |
| Inhalt: | 692 S. |
| ISBN-13: | 9781119152729 |
| ISBN-10: | 1119152720 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: |
Tattar, Prabhanjan N
Ramaiah, Suresh Manjunath, B G |
| Hersteller: |
Wiley
John Wiley & Sons |
| Maße: | 250 x 175 x 41 mm |
| Von/Mit: | Prabhanjan N Tattar (u. a.) |
| Erscheinungsdatum: | 02.05.2016 |
| Gewicht: | 1,355 kg |
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