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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