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【書名】Statistical Evidence: A Likelihood paradigm
【著者】Richard Royall
【刊行】1997年
【出版】Chapman & Hall / CRC, Boca Raton
【叢書】Monographs on Statistics and Applied Probability 71
【頁数】xvi+191 pp.
【定価】不明
【ISBN】0-412-04411-0
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【目次】
Preface xi
1. The first principle 1
1.1 Introduction
1.2 The law of likelihood
1.3 Three questions
1.4 Towards verification
1.5 Relativity of evidence
1.6 Strength of evidence
1.7 Counterexamples
1.8 Testing simple hypotheses
1.9 Composite hypotheses
1.10 Another counterexample
1.11 Irrelevance of the sample space
1.12 The likelihood principle
1.13 Evidence and uncertainty
1.14 Summary
Exercises
2. Neyman-Pearson theory 35
2.1 Introduction
2.2 Neyman-Pearson statistical theory
2.3 Evidential interpretation of the results of
Neyman-Pearson decision procedures
2.4 Neyman-Pearson hypothesis testing in planning experiments:
Choosing the sample size
2.5 Summary
Exercises
3. Fisherian theory 61
3.1 Introduction
3.2 A method for measuring statistical evidence:
The test of significance
3.3 The rationale for significance tests
3.4 Troubles with p-values
3.5 Rejection trials
3.6 A sample of interpretations
3.7 The illogic of rejection trials
3.8 Confidence sets from rejection trials
3.9 Alternative hypotheses in science
3.10 Summary
Exercises
4. Paradigms for statistics 83
4.1 Introduction
4.2 Three paradigms
4.3 An alternative paradigm
4.4 Probabilities of weak and misleading evidence
4.5 Understanding the likelihood paradism
4.6 Evidence about a probability: Planning a clinical trial
and interpreting the results
4.7 Summary
Exercises
5. Resolving the paradoxes from the old paradigm 109
5.1 Introduction
5.2 Why ia a power of only 0.80 OK?
5.3 Peeking at data: repeated tests
5.4 Testing more than one hypotheses.
5.5 What is wrong with one-sided tests?
5.6 Why not use the most powerful test?
5.7 Must the significance level be predetermined?
And is the strength of evidence limited by
the researcher's expectations?
5.8 Summary
Exercises
6. Looking at likelihoods 123
6.1 Introduction
6.2 Evidence about hazard rates in two factories
6.3 Evidence about an odds ratio
6.4 A standardized mortality ratio
6.5 Evidence about a finite population total
6.6 Determinants of plans to attend college
6.7 Evidence about probabilities in a 2x2x2x2 table
6.8 Evidence from a community intervention study of hypertension
6.9 Effects of sugars on growth of pea sections:
Analysis of variance
6.10 Summary
7. Nuisance parameters 151
7.1 Introduction
7.2 Orthogonal parameters
7.3 Marginal likelihoods
7.4 Conditional likelihoods
7.5 Estimated likelihoods
7.6 Profile likelihoods
7.7 Synthetic conditional likelihoods
7.8 Summary
Exercises
8. Bayesian statistical inference 167
8.1 Introduction
8.2 Bayesian statistical models
8.3 Subjectivity in Bayesian medels
8.4 The trouble with Bayesian statistics
8.5 Are likelihood methods Bayesian?
8.6 Objective Bayesian inference
8.7 Bayesian integrated likelihoods
8.8 Summary
Exercises
Appendix: The paradox of the ravens 177
References 181
Index 189
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