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
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