Statistical evidence: a likelihood paradigm
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman & Hall
1997
|
| Edition: | 1. ed. |
| Series: | Monographs on statistics and applied probability
71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 191 S. graph. Darst. |
| ISBN: | 0412044110 |
Staff View
MARC
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| 100 | 1 | |a Royall, Richard M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical evidence |b a likelihood paradigm |c Richard M. Royall |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 The first principle 1
1.1 Introduction 1
1.2 The law of likelihood 1
1.3 Three questions 3
1.4 Towards verification 5
1.5 Relativity of evidence 8
1.6 Strength of evidence 11
1.7 Counterexamples 13
1.8 Testing simple hypotheses 16
1.9 Composite hypotheses 17
1.10 Another counterexample 20
1.11 Irrelevance of the sample space 22
1.12 The likelihood principle 24
1.13 Evidence and uncertainty 28
1.14 Summary 31
Exercises 31
2 Neyman Pearson theory 35
2.1 Introduction 35
2.2 Neyman Pearson statistical theory 35
2.3 Evidential interpretation of the results of
Neyman Pearson decision procedures 41
2.4 Neyman Pearson hypothesis testing in planning
experiments: choosing the sample size 50
2.5 Summary 58
Exercises 58
3 Fisherian theory 61
3.1 Introduction 61
3.2 A method for measuring statistical evidence:
the test of significance 61
viii CONTENTS
3.3 The rationale for significance tests 65
3.4 Troubles with p values 68
3.5 Rejection trials 71
3.6 A sample of interpretations 76
3.7 The illogic of rejection trials 77
3.8 Confidence sets from rejection trials 78
3.9 Alternative hypotheses in science 79
3.10 Summary 81
Exercises 81
4 Paradigms for statistics 83
4.1 Introduction 83
4.2 Three paradigms 83
4.3 An alternative paradigm 88
4.4 Probabilities of weak and misleading evidence:
normal distribution mean 90
4.5 Understanding the likelihood paradigm 94
4.6 Evidence about a probability: planning a clinical
trial and interpreting the results 97
4.7 Summary 107
Exercise 108
5 Resolving the paradoxes from the old paradigms 109
5.1 Introduction 109
5.2 Why is a power of only 0.80 OK? 109
5.3 Peeking at data: repeated tests 111
5.4 Testing more than one hypothesis 113
5.5 What is wrong with one sided tests? 116
5.6 Why not use the most powerful test? 117
5.7 Must the significance level be predetermined?
And is the strength of evidence limited by the
researcher s expectations? 119
5.8 Summary 121
Exercises 121
6 Looking at likelihoods 123
6.1 Introduction 123
6.2 Evidence about hazard rates in two factories 124
6.3 Evidence about an odds ratio 126
6.4 A standardized mortality ratio 129
6.5 Evidence about a finite population total 130
6.6 Determinants of plans to attend college 134
CONTENTS ix
6.7 Evidence about probabilities ina2x2x2x2 table 137
6.8 Evidence from a community intervention study of
hypertension 141
6.9 Effects of sugars on growth of pea sections:
analysis of variance 143
6.10 Summary 149
7 Nuisance parameters 151
7.1 Introduction 151
7.2 Orthogonal parameters 152
7.3 Marginal likelihoods 154
7.4 Conditional likelihoods 155
7.5 Estimated likelihoods 158
7.6 Profile likelihoods 158
7.7 Synthetic conditional likelihoods 159
7.8 Summary 161
Exercises 161
8 Bayesian statistical inference 167
8.1 Introduction 167
8.2 Bayesian statistical models 167
8.3 Subjectivity in Bayesian models 169
8.4 The trouble with Bayesian statistics 171
8.5 Are likelihood methods Bayesian? 172
8.6 Objective Bayesian inference 173
8.7 Bayesian integrated likelihoods 174
8.8 Summary 175
Exercises 176
Appendix: The paradox of the ravens 177
References 181
Index 189
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:40Z |
| institution | BVB |
| isbn | 0412044110 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007644145 |
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| physical | XVI, 191 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Royall, Richard M. Verfasser aut Statistical evidence a likelihood paradigm Richard M. Royall 1. ed. London [u.a.] Chapman & Hall 1997 XVI, 191 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 71 Estimation, Théorie de l' Estimation, Théorie de l' ram ORTHOGONALITE inriac Probabilités Probabilités ram Statistique mathématique Statistische toetsen gtt Waarschijnlijkheidstheorie gtt inférence statistique inriac modèle bayesien inriac paradigme inriac probabilité inriac Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf Maximum-Likelihood-Schätzung (DE-588)4194624-8 s DE-604 Monographs on statistics and applied probability 71 (DE-604)BV002494005 71 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007644145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Royall, Richard M. Statistical evidence a likelihood paradigm Monographs on statistics and applied probability Estimation, Théorie de l' Estimation, Théorie de l' ram ORTHOGONALITE inriac Probabilités Probabilités ram Statistique mathématique Statistische toetsen gtt Waarschijnlijkheidstheorie gtt inférence statistique inriac modèle bayesien inriac paradigme inriac probabilité inriac Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| subject_GND | (DE-588)4194624-8 |
| title | Statistical evidence a likelihood paradigm |
| title_auth | Statistical evidence a likelihood paradigm |
| title_exact_search | Statistical evidence a likelihood paradigm |
| title_full | Statistical evidence a likelihood paradigm Richard M. Royall |
| title_fullStr | Statistical evidence a likelihood paradigm Richard M. Royall |
| title_full_unstemmed | Statistical evidence a likelihood paradigm Richard M. Royall |
| title_short | Statistical evidence |
| title_sort | statistical evidence a likelihood paradigm |
| title_sub | a likelihood paradigm |
| topic | Estimation, Théorie de l' Estimation, Théorie de l' ram ORTHOGONALITE inriac Probabilités Probabilités ram Statistique mathématique Statistische toetsen gtt Waarschijnlijkheidstheorie gtt inférence statistique inriac modèle bayesien inriac paradigme inriac probabilité inriac Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| topic_facet | Estimation, Théorie de l' ORTHOGONALITE Probabilités Statistique mathématique Statistische toetsen Waarschijnlijkheidstheorie inférence statistique modèle bayesien paradigme probabilité Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung |
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