统计推断原理

1 Preliminaries

Summary

1.1 Starting point

1.2 Role of formal theory of inference

1.3 Some simple models

1.4 Formulation of objectives

1.5 Two broad approaches to statistical inference

1.6 Some further discussion

1.7 Parameters

Notes 1

2 Some concepts and simple applications

Summary

2.1 Likelihood

2.2 Sufficiency

2.3 Exponential family

2.4 Choice of priors for exponential family problems

2.5 Simple frequentist discussion

2.6 Pivots

Notes 2

3 Significance tests

Summary

3.1 General remarks

3.2 Simple significance test

3.3 One- and two-sided tests

3.4 Relation with acceptance and rejection

3.5 Formulation of alternatives and test statistics

3.6 Relation with interval estimation

3.7 Interpretation of significance tests

3.8 Bayesian testing

Notes 3

4 More complicated situations

Summary

4.1 General remarks

4.2 General Bayesian formulation

4.3 Frequentist analysis

4.4 Some more general frequentist developments

4.5 Some further Bayesian examples

Notes 4

5 Interpretations of uncertainty

Summary

5.1 General remarks

5.2 Broad roles of probability

5.3 Frequentist interpretation of upper limits

5.4 Neyman-Pearson operational criteria

5.5 Some general aspects of the frequentist approach

5.6 Yet more on the frequentist approach

5.7 Personalistic probability

5.8 Impersonal degree of belief

5.9 Reference priors

5.10 Temporal coherency

5.11 Degree of belief and frequency

5.12 Statistical implementation of Bayesian analysis

5.13 Model uncertainty

5.14 Consistency of data and prior

5.15 Relevance of frequentist assessment

5.16 Sequential stopping

5.17 A simple classification problem

Notes 5

6 Asymptotic theory

Summary

6.1 General remarks

6.2 Scalar parameter

6.3 Multidimensional parameter

6.4 Nuisance parameters

6.5 Tests and model reduction

6.6 Comparative discussion

6.7 Profile likelihood as an information summarizer

6.8 Constrained estimation

6.9 Semi-asymptotic arguments

6.10 Numerical-analytic aspects

6.11 Higher-order asymptotics

Notes 6

7 Further aspects of maximum likelihood

Summary

7.1 Multimodal likelihoods

7.2 Irregular form

7.3 Singular information matrix

7.4 Failure of model

7.5 Unusual parameter space

7.6 Modified likelihoods

Notes 7

8 Additional objectives

Summary

8.1 Prediction

8.2 Decision analysis

8.3 Point estimation

8.4 Non-likelihood-based methods

Notes 8

9 Randomization-based analysis

Summary

9.1 General remarks

9.2 Sampling a finite population

9.3 Design of experiments

Notes 9

Appendix A： A brief history

Appendix B： A personal view

References

Author index

Subject index

《统计推断原理(英文版)》是统计学名家名作，包含9章内容和两个附录，前面几章介绍一些基本概念，如参数、似然、主元等，然后介绍显著性检验、渐进理论以及比较复杂的统计推断问题。还特别介绍了实验设计中基于随机化的统计推断。核心概念的解释非常清晰，即使跳过其中的数学细节，也能使读者理解。
　　《统计推断原理(英文版)》可作为工科、管理类学科专业本科生、研究生的教材或参考书，也可供教师、工程技术人员自学之用。

《统计推断原理(英文版)》是在现代统计学之父Cox授课讲义内容的基础上成形的，系统地介绍了统计推断的理论，既涵盖了传统的频率统计学。又囊括了现代的贝叶斯统计学。除介绍了统计推断的重要概念如参数。似然、主元等之外。还阐述了显著性检验。渐进理论以及较复杂的统计推断问题，并特别介绍了实验设计中基于随机化的统计推断。对于核心概念的解释非常清晰，读者即使跳过其中的数学细节，也能理解有关概念。