Produktbild: Introduction to Bayesian Statistics

Introduction to Bayesian Statistics 3rd Edition

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.10.2016

Verlag

John Wiley & Sons

Seitenzahl

624

Maße (L/B/H)

24/16.1/3.7 cm

Gewicht

1085 g

Auflage

3rd edition

Sprache

Englisch

ISBN

978-1-118-09156-2

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

03.10.2016

Verlag

John Wiley & Sons

Seitenzahl

624

Maße (L/B/H)

24/16.1/3.7 cm

Gewicht

1085 g

Auflage

3rd edition

Sprache

Englisch

ISBN

978-1-118-09156-2

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Introduction to Bayesian Statistics
  • Preface xiii

    1 Introduction to Statistical Science 1

    1.1 The Scientic Method: A Process for Learning 3

    1.2 The Role of Statistics in the Scientic Method 5

    1.3 Main Approaches to Statistics 5

    1.4 Purpose and Organization of This Text 8

    2 Scientic Data Gathering 13

    2.1 Sampling from a Real Population 14

    2.2 Observational Studies and Designed Experiments 17

    Monte Carlo Exercises 23

    3 Displaying and Summarizing Data 31

    3.1 Graphically Displaying a Single Variable 32

    3.2 Graphically Comparing Two Samples 39

    3.3 Measures of Location 41

    3.4 Measures of Spread 44

    3.5 Displaying Relationships Between Two or More Variables 46

    3.6 Measures of Association for Two or More Variables 49

    Exercises 52

    4 Logic, Probability, and Uncertainty 59

    4.1 Deductive Logic and Plausible Reasoning 60

    4.2 Probability 62

    4.3 Axioms of Probability 64

    4.4 Joint Probability and Independent Events 65

    4.5 Conditional Probability 66

    4.6 Bayes' Theorem 68

    4.7 Assigning Probabilities 74

    4.8 Odds and Bayes Factor 75

    4.9 Beat the Dealer 76

    Exercises 80

    5 Discrete Random Variables 83

    5.1 Discrete Random Variables 84

    5.2 Probability Distribution of a Discrete Random Variable 86

    5.3 Binomial Distribution 90

    5.4 Hypergeometric Distribution 92

    5.5 Poisson Distribution 93

    5.6 Joint Random Variables 96

    5.7 Conditional Probability for Joint Random Variables 100

    Exercises 104

    6 Bayesian Inference for Discrete Random Variables 109

    6.1 Two Equivalent Ways of Using Bayes' Theorem 114

    6.2 Bayes' Theorem for Binomial with Discrete Prior 116

    6.3 Important Consequences of Bayes' Theorem 119

    6.4 Bayes' Theorem for Poisson with Discrete Prior 120

    Exercises 122

    Computer Exercises 126

    7 Continuous Random Variables 129

    7.1 Probability Density Function 131

    7.2 Some Continuous Distributions 135

    7.3 Joint Continuous Random Variables 143

    7.4 Joint Continuous and Discrete Random Variables 144

    Exercises 147

    8 Bayesian Inference for Binomial Proportion 149

    8.1 Using a Uniform Prior 150

    8.2 Using a Beta Prior 151

    8.3 Choosing Your Prior 154

    8.4 Summarizing the Posterior Distribution 158

    8.5 Estimating the Proportion 161

    8.6 Bayesian Credible Interval 162

    Exercises 164

    Computer Exercises 167

    9 Comparing Bayesian and Frequentist Inferences for Proportion 169

    9.1 Frequentist Interpretation of Probability and Parameters 170

    9.2 Point Estimation 171

    9.3 Comparing Estimators for Proportion 174

    9.4 Interval Estimation 175

    9.5 Hypothesis Testing 178

    9.6 Testing a One-Sided Hypothesis 179

    9.7 Testing a Two-Sided Hypothesis 182

    Exercises 187

    Monte Carlo Exercises 190

    10 Bayesian Inference for Poisson 193

    10.1 Some Prior Distributions for Poisson 194

    10.2 Inference for Poisson Parameter 200

    Exercises 207

    Computer Exercises 208

    11 Bayesian Inference for Normal Mean 211

    11.1 Bayes' Theorem for Normal Mean with a Discrete Prior 211

    11.2 Bayes' Theorem for Normal Mean with a Continuous Prior 218

    11.3 Choosing Your Normal Prior 222

    11.4 Bayesian Credible Interval for Normal Mean 224

    11.5 Predictive Density for Next Observation 227

    Exercises 230

    Computer Exercises 232

    12 Comparing Bayesian and Frequentist Inferences for Mean 237

    12.1 Comparing Frequentist and Bayesian Point Estimators 238

    12.2 Comparing Condence and Credible Intervals for Mean 241

    12.3 Testing a One-Sided Hypothesis about a Normal Mean 243

    12.4 Testing a Two-Sided Hypothesis about a Normal Mean 247

    Exercises 251

    13 Bayesian Inference for Di erence Between Means 255

    13.1 Independent Random Samples from Two Normal Distributions 256

    13.2 Case 1: Equal Variances 257

    13.3 Case 2: Unequal Variances 262

    13.4 Bayesian Inference for Dierence Between Two Proportions Using Normal Approximation 265

    13.5 Normal Random Samples from Paired Experiments 266

    Exercises 272

    14 Bayesian Inference for Simple Linear Regression 283

    14.1 Least Squares Regression 284

    14.2 Exponential Growth Model 288

    14.3 Simple Linear Regression Assumptions 290

    14.4 Bayes' Theorem for the Regression Model 292

    14.5 Predictive Distribution for Future Observation 298

    Exercises 303

    Computer Exercises 312

    15 Bayesian Inference for Standard Deviation 315

    15.1 Bayes' Theorem for Normal Variance with a Continuous Prior 316

    15.2 Some Specic Prior Distributions and the Resulting Posteriors 318

    15.3 Bayesian Inference for Normal Standard Deviation 326

    Exercises 332

    Computer Exercises 335

    16 Robust Bayesian Methods 337

    16.1 Eect of Misspecied Prior 338

    16.2 Bayes' Theorem with Mixture Priors 340

    Exercises 349

    Computer Exercises 351

    17 Bayesian Inference for Normal with Unknown Mean and Variance 355

    17.1 The Joint Likelihood Function 358

    17.2 Finding the Posterior when Independent Jeffreys' Priors for ¿ and ¿2 Are Used 359

    17.3 Finding the Posterior when a Joint Conjugate Prior for ¿ and ¿2 Is Used 361

    17.4 Difference Between Normal Means with Equal Unknown Variance 367

    17.5 Difference Between Normal Means with Unequal Unknown Variances 377

    Computer Exercises 383

    Appendix: Proof that the Exact Marginal Posterior Distribution of ¿ is Student's t 385

    18 Bayesian Inference for Multivariate Normal Mean Vector 393

    18.1 Bivariate Normal Density 394

    18.2 Multivariate Normal Distribution 397

    18.3 The Posterior Distribution of the Multivariate Normal Mean Vector when Covariance Matrix Is Known 398

    18.4 Credible Region for Multivariate Normal Mean Vector when Covariance Matrix Is Known 400

    18.5 Multivariate Normal Distribution with Unknown Covariance Matrix 402

    Computer Exercises 406

    19 Bayesian Inference for the Multiple Linear Regression Model 411

    19.1 Least Squares Regression for Multiple Linear Regression Model 412

    19.2 Assumptions of Normal Multiple Linear Regression Model 414

    19.3 Bayes' Theorem for Normal Multiple Linear Regression Model 415

    19.4 Inference in the Multivariate Normal Linear Regression Model 419

    19.5 The Predictive Distribution for a Future Observation 425

    Computer Exercises 428

    20 Computational Bayesian Statistics Including Markov Chain Monte Carlo 431

    20.1 Direct Methods for Sampling from the Posterior 436

    20.2 Sampling - Importance - Resampling 450

    20.3 Markov Chain Monte Carlo Methods 454

    20.4 Slice Sampling 470

    20.5 Inference from a Posterior Random Sample 473

    20.6 Where to Next? 475

    A Introduction to Calculus 477

    B Use of Statistical Tables 497

    C Using the Included Minitab Macros 523

    D Using the Included R Functions 543

    E Answers to Selected Exercises 565

    References 591

    Index 595