Probability and statistical inference. (2020)

• Record Type: Book
• Further Information: Note: Robert Bartoszynski and Magdalena Niewiadomska-Bugaj.
• Authors: Bartoszyński, Robert; Niewiadomska-Bugaj, Magdalena
• Contents: Preface vii Preface vi 1 Experiments, Sample Spaces, and Events 1 1.1 Introduction 1 1.2 Sample Space 2 1.3 Algebra of Events 9 1.4 Infinite Operations on Events 15 2 Probability 25 2.1 Introduction 25 2.2 Probability as a Frequency 25 2.3 Axioms of Probability 26 2.4 Consequences of the Axioms 31 2.5 Classical Probability 35 2.6 Necessity of the Axioms* 36 2.7 Subjective Probability* 41 3 Counting 45 3.1 Introduction 45 3.2 Product Sets, Orderings, and Permutations 45 3.3 Binomial Coefficients 51 3.4 Multinomial Coefficients 64 4 Conditional Probability, Independence, and Markov Chains 67 4.1 Introduction 67 4.2 Conditional Probability 68 4.3 Partitions; Total Probability Formula 74 4.4 Bayes’ Formula 79 4.5 Independence 84 4.6 Exchangeability; Conditional Independence 90 4.7 Markov Chains* 93 5 Random Variables: Univariate Case 107 5.1 Introduction 107 5.2 Distributions of Random Variables 108 5.3 Discrete and Continuous Random Variables 117 5.4 Functions of Random Variables 129 5.5 Survival and Hazard Functions 136 6 Random Variables: Multivariate Case 141 6.1 Bivariate Distributions 141 6.2 Marginal Distributions; Independence 148 6.3 Conditional Distributions 160 6.4 Bivariate Transformations 167 6.5 Multidimensional Distributions 176 7 Expectation 183 7.1 Introduction 183 7.2 Expected Value 184 7.3 Expectation as an Integral* 192 7.4 Properties of Expectation 199 7.5 Moments 207 7.6 Variance 215 7.7 Conditional Expectation 227 7.8 Inequalities 231 8 Selected Families of Distributions 237 8.1 Bernoulli Trials and Related Distributions 237 8.2 Hypergeometric Distribution 251 8.3 Poisson Distribution and Poisson Process 256 8.4 Exponential, Gamma and Related Distributions 269 8.5 Normal Distribution 276 8.6 Beta Distribution 286 9 Random Samples 293 9.1 Statistics and Sampling Distributions 293 9.2 Distributions Related to Normal 295 9.3 Order Statistics 300 9.4 Generating Random Samples 307 9.5 Convergence 312 9.6 Central Limit Theorem 322 10 Introduction to Statistical Inference 331 10.1 Overview 331 10.2 Basic Models 334 10.3 Sampling 336 10.4 Measurement Scales 342 11 Estimation 347 11.1 Introduction 347 11.2 Consistency 352 11.3 Loss, Risk, and Admissibility 355 11.4 Efficiency 361 11.5 Methods of Obtaining Estimators 368 11.6 Sufficiency 387 11.7 Interval Estimation 403 12 Testing Statistical Hypotheses 419 12.1 Introduction 419 12.2 Intuitive Background 423 12.3 Most Powerful Tests 432 12.4 Uniformly Most Powerful Tests 445 12.5 Unbiased Tests 452 12.6 Generalized Likelihood Ratio Tests 456 12.7 Conditional Tests 463 12.8 Tests and Confidence Intervals 466 12.9 Review of Tests for Normal Distributions 467 12.10 Monte Carlo, Bootstrap, and Permutation Tests 477 14 Linear Models 483 14.1 Introduction 483 14.2 Regression of the First and Second Kind 485 14.3 Distributional Assumptions 491 14.4 Linear Regression in the Normal Case 494 14.5 Testing Linearity 500 14.6 Prediction 503 14.7 Inverse Regression 505 14.8 BLUE 508 14.9 Regression Toward the Mean 510 14.10 Analysis of Variance 512 14.11 One-Way Layout 512 14.12 Two-Way Layout 516 14.13 ANOVA Models with Interaction 518 14.14 Further Extensions 522 15 Rank Methods 525 15.1 Introduction 525 15.2 Glivenko-Cantelli Theorem 526 15.3 Kolmogorov-Smirnov Tests 530 15.4 One-Sample Rank Tests 537 15.5 Two-Sample Rank Tests 544 15.6 Kruskal-Wallis Test 548 16 Analysis of Categorical Data 551 16.1 Introduction 551 16.2 Chi-Square Tests 553 16.3 Homogeneity and Independence 559 16.4 Consistency and Power 565 16.5 2×2 Contingency Tables 570 16.6 r × c Contingency Tables 578 17 Basics of Bayesian Statistics 583 17.1 Introduction 583 17.2 Prior and Posterior Distributions 584 17.3 Bayesian Inference 592 17.4 Final Comments 608 Appendix 1 609 Appendix 2 616 Bibliography 619 Answers to Odd-Numbered Problems 624 Index 632 Index 632
• Edition: Third edition
• Publisher Details: New York : Wiley-Interscience
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 519.54; Probabilities; Mathematical statistics
• Languages: English
• ISBNs: 9781119243823; 9781119243816
• Related ISBNs: 9781119243809
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.