Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 2
Table of Contents
Оглавление1 Cover
2 Wiley Series in Probability and Statistics
3 Probability and Statistical Inference
9 Chapter 1: Experiments, Sample Spaces, and Events 1.1 Introduction 1.2 Sample Space 1.3 Algebra of Events 1.4 Infinite Operations on Events Notes
10 Chapter 2: Probability 2.1 Introduction 2.2 Probability as a Frequency 2.3 Axioms of Probability 2.4 Consequences of the Axioms 2.5 Classical Probability 2.6 Necessity of the Axioms* 2.7 Subjective Probability* Note
11 Chapter 3: Counting 3.1 Introduction 3.2 Product Sets, Orderings, and Permutations 3.3 Binomial Coefficients 3.4 Multinomial Coefficients Notes
12 Chapter 4: Conditional Probability, Independence, and Markov Chains 4.1 Introduction 4.2 Conditional Probability 4.3 Partitions; Total Probability Formula 4.4 Bayes' Formula 4.5 Independence 4.6 Exchangeability; Conditional Independence 4.7 Markov Chains* Note
13 Chapter 5: Random Variables: Univariate Case 5.1 Introduction 5.2 Distributions of Random Variables 5.3 Discrete and Continuous Random Variables 5.4 Functions of Random Variables 5.5 Survival and Hazard Functions Notes
14 Chapter 6: Random Variables: Multivariate Case 6.1 Bivariate Distributions 6.2 Marginal Distributions; Independence 6.3 Conditional Distributions 6.4 Bivariate Transformations 6.5 Multidimensional Distributions
15 Chapter 7: Expectation 7.1 Introduction 7.2 Expected Value 7.3 Expectation as an Integral* 7.4 Properties of Expectation 7.5 Moments 7.6 Variance 7.7 Conditional Expectation 7.8 Inequalities
16 Chapter 8: Selected Families of Distributions 8.1 Bernoulli Trials and Related Distributions 8.2 Hypergeometric Distribution 8.3 Poisson Distribution and Poisson Process 8.4 Exponential, Gamma, and Related Distributions 8.5 Normal Distribution 8.6 Beta Distribution Notes
17 Chapter 9: Random Samples 9.1 Statistics and Sampling Distributions 9.2 Distributions Related to Normal 9.3 Order Statistics 9.4 Generating Random Samples 9.5 Convergence 9.6 Central Limit Theorem Notes
18 Chapter 10: Introduction to Statistical Inference 10.1 Overview 10.2 Basic Models 10.3 Sampling 10.4 Measurement Scales Notes
19 Chapter 11: Estimation 11.1 Introduction 11.2 Consistency 11.3 Loss, Risk, and Admissibility 11.4 Efficiency 11.5 Methods of Obtaining Estimators 11.6 Sufficiency 11.7 Interval Estimation Notes
20 Chapter 12: Testing Statistical Hypotheses 12.1 Introduction 12.2 Intuitive Background 12.3 Most Powerful Tests 12.4 Uniformly Most Powerful Tests 12.5 Unbiased Tests 12.6 Generalized Likelihood Ratio Tests 12.7 Conditional Tests 12.8 Tests and Confidence Intervals 12.9 Review of Tests for Normal Distributions 12.10 Monte Carlo, Bootstrap, and Permutation Tests Notes
21 Chapter 13: Linear Models 13.1 Introduction 13.2 Regression of the First and Second Kind 13.3 Distributional Assumptions 13.4 Linear Regression in the Normal Case 13.5 Testing Linearity 13.6 Prediction 13.7 Inverse Regression 13.8 BLUE 13.9 Regression Toward the Mean 13.10 Analysis of Variance 13.11 One‐Way Layout 13.12 Two‐Way Layout 13.13 ANOVA Models with Interaction 13.14 Further Extensions Notes
22 Chapter 14: Rank Methods 14.1 Introduction 14.2 Glivenko–Cantelli Theorem 14.3 Kolmogorov–Smirnov Tests 14.4 One‐Sample Rank Tests 14.5 Two‐Sample Rank Tests 14.6 Kruskal–Wallis Test Note
23 Chapter 15: Analysis of Categorical Data 15.1 Introduction 15.2 Chi‐Square Tests 15.3 Homogeneity and Independence 15.4 Consistency and Power 15.5 2 x 2 Contingency Tables 15.6 R x C Contingency Tables
24 Chapter 16: Basics of Bayesian Statistics 16.1 Introduction 16.2 Prior and Posterior Distributions 16.3 Bayesian Inference 16.4 Final Comments Notes
25 APPENDIX A: APPENDIX ASupporting R Code
26 APPENDIX B: APPENDIX BStatistical Tables
27 Bibliography
28 Answers to Odd‐Numbered Problems
29 Index
