Example 1.1 The normal mean

Example 1.2 Linear regression

Example 1.3 Linear regression in semiparametric form

Example 1.4 Linear model

Example 1.5 Normal theory nonlinear regression

Example 1.6 Exponential distribution

Example 1.7 Comparison of binomial probabilities

Example 1.8 Location and related problems

Example 1.9 A component of variance model

Example 1.10 Markov models

Example 2.1 Exponential distribution(ctd)

Example 2.2 Linear model(ctd)

Example 2.3 Uniform distribution

Example 2.4 Binary fission

Example 2.5 Binomial distribution

Example 2.6 Fisher's hyperbola

Example 2.7 Binary fission(ctd)

Example 2.8 Binomial distribution(ctd)

Example 2.9 Mean of a multivariate normal distribution

Example 3.1 Test of a Poissonmean

Example 3.2 Adequacy of Poisson model

Example 3.3 More on the Poisson distribution

Example 3.4 Test of symmetry

Example 3.5 Nonparametric two-sample test

Example 3.6 Ratio of normal means

Example 3.7 Poisson-distributed signal with additive noise

Example 4.1 Uniform distribution of known range

Example 4.2 Two measuring instruments

Example 4.3 Linear model

Example 4.4 Two-by-two contingency table

Example 4.5 Mantel-Haenszel procedure

Example 4.6 Simple regression for binary data

Example 4.7 Normal mean,variance unknown

Example 4.8 Comparison of gamma distributions

Example 4.9 Unacceptable conditioning

Example 4.10 Location model

Example 4.11 Normal mean,variance unknown(ctd)

Example 4.12 Normal variance

Example 4.13 Normal mean,variance unknown(ctd)

Example 4.14 Components of variance

Example 5.1 Exchange paradox

Example 5.2 Two measuring instruments(ctd)

Example 5.3 Rainy days in Gothenburg

Example 5.4 The normal mean(ctd)

Example 5.5 The noncentral chi-squared distribution

Example 5.6 A set of binomial probabilities

Example 5.7 Exponential regression

Example 5.8 Components of variance(ctd)

Example 5.9 Bias assessment

Example 5.10 Selective reporting

Example 5.11 Precision-based choice of sample size

Example 5.12 Sampling the Poisson process

Example 5.13 Multivariate normal distributions

Example 6.1 Location model(ctd)

Example 6.2 Exponential family

Example 6.3 Transformation to near location form

Example 6.4 Mixed parameterization of the exponential family

Example 6.5 Proportional hazards Weibull model

Example 6.6 A right-censored normal distribution

Example 6.7 Random walk with an absorbing barrier

Example 6.8 Curved exponential family model

Example 6.9 Covariance selection model

Example 6.10 Poisson-distributed signal with estimated background

Example 7.1 An unbounded likelihood

Example 7.2 Uniform distribution

Example 7.3 Densities with power-law contact

Example 7.4 Model of hidden periodicity

Example 7.5 A special nonlinear regression

Example 7.6 Informative nonresponse

Example 7.7 Integer normal mean

Example 7.8 Mixture of two normal distributions

Example 7.9 Normal-theory linear model with many parameters

Example 7.10 A non-normal illustration

Example 7.11 Parametric model for right-censored failure data

Example 7.12 A fairly general stochastic process

Example 7.13 Semiparametric model for censored failure data

Example 7.14 Lag one correlation of a stationary Gaussian time series

Example 7.15 A long binary sequence

Example 7.16 Case-control study

Example 8.1 A new observation from a normal distribution

Example 8.2 Exponential family

Example 8.3 Correlation between different estimates

Example 8.4 The sign test

Example 8.5 Unbiased estimate of standard deviation

Example 8.6 Summarization of binary risk comparisons

Example 8.7 Brownian motion

Example 9.1 Two-by-two contingency table

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 Reladon 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

Notes4

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：Apersonal view

References

Author index

Subject index