Principles of statistical inference:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 219 S. graph. Darst. |
| ISBN: | 9780521866736 0521866731 9780521685672 0521685672 |
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| 245 | 1 | 0 | |a Principles of statistical inference |c D. R. Cox |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
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Datensatz im Suchindex
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| adam_text | Contents
List of examples ix
Preface xiii
1 Preliminaries 1
Summary 1
1.1 Starting point ]
1.2 Role of formal theory of inference 3
1.3 Some simple models 3
1.4 Formulation of objectives 7
1.5 Two broad approaches to statistical inference 7
1.6 Some further discussion 10
1.7 Parameters 13
Notes 1 14
2 Some concepts and simple applications 17
Summary 17
2.1 Likelihood 17
2.2 Sufficiency 18
2.3 Exponential family 20
2.4 Choice of priors for exponential family problems 23
2.5 Simple frequentist discussion 24
2.6 Pivots 25
Notes 2 27
3 Significance tests 30
Summary 30
3.1 General remarks 30
3.2 Simple significance test 31
3.3 One and two sided tests 35
3.4 Relation with acceptance and rejection 36
3.5 Formulation of alternatives and test statistics 36
3.6 Relation with interval estimation 40
3.7 Interpretation of significance tests 41
3.8 Bayesian testing 42
Notes 3 43
4 More complicated situations 45
Summary 45
4.1 General remarks 45
4.2 General Bayesian formulation 45
4.3 Frequentist analysis 47
4.4 Some more general frequentist developments 50
4.5 Some further Bayesian examples 59
Notes 4 62
5 Interpretations of uncertainty 64
Summary 64
5.1 General remarks 64
5.2 Broad roles of probability 65
5.3 Frequentist interpretation of upper limits 66
5.4 Neyman Pearson operational criteria 68
5.5 Some general aspects of the frequentist approach 68
5.6 Yet more on the frequentist approach 69
5.7 Personalistic probability 71
5.8 Impersonal degree of belief 73
5.9 Reference priors 76
5.10 Temporal coherency 78
5.11 Degree of belief and frequency 79
5.12 Statistical implementation of Bayesian analysis 79
5.13 Model uncertainty 84
5.14 Consistency of data and prior 85
5.15 Relevance of frequentist assessment 85
5.16 Sequential stopping 88
5.17 A simple classification problem 91
Notes 5 93
6 Asymptotic theory 96
Summary 96
6.1 General remarks 96
6.2 Scalar parameter 97
6.3 Multidimensional parameter 107
6.4 Nuisance parameters 109
6.5 Tests and model reduction 114
6.6 Comparative discussion 117
6.7 Profile likelihood as an information summarizer 119
6.8 Constrained estimation 120
6.9 Semi asymptotic arguments 124
6.10 Numerical analytic aspects 125
6.11 Higher order asymptotics 128
Notes 6 130
7 Further aspects of maximum likelihood 133
Summary 133
7.1 Multimodal likelihoods 133
7.2 Irregular form 135
7.3 Singular information matrix 139
7.4 Failure of model 141
7.5 Unusual parameter space 142
7.6 Modified likelihoods 144
Notes 7 159
8 Additional objectives 161
Summary 161
8.1 Prediction 161
8.2 Decision analysis 162
8.3 Point estimation 163
8.4 Non likelihood based methods 169
Notes 8 175
9 Randomization based analysis 178
Summary 178
9.1 General remarks 178
9.2 Sampling a finite population 179
9.3 Design of experiments 184
Notes 9 192
Appendix A: A brief history 194
Appendix B: A personal view 197
References 201
Author index 209
Subject index 213
|
| adam_txt |
Contents
List of examples ix
Preface xiii
1 Preliminaries 1
Summary 1
1.1 Starting point ]
1.2 Role of formal theory of inference 3
1.3 Some simple models 3
1.4 Formulation of objectives 7
1.5 Two broad approaches to statistical inference 7
1.6 Some further discussion 10
1.7 Parameters 13
Notes 1 14
2 Some concepts and simple applications 17
Summary 17
2.1 Likelihood 17
2.2 Sufficiency 18
2.3 Exponential family 20
2.4 Choice of priors for exponential family problems 23
2.5 Simple frequentist discussion 24
2.6 Pivots 25
Notes 2 27
3 Significance tests 30
Summary 30
3.1 General remarks 30
3.2 Simple significance test 31
3.3 One and two sided tests 35
3.4 Relation with acceptance and rejection 36
3.5 Formulation of alternatives and test statistics 36
3.6 Relation with interval estimation 40
3.7 Interpretation of significance tests 41
3.8 Bayesian testing 42
Notes 3 43
4 More complicated situations 45
Summary 45
4.1 General remarks 45
4.2 General Bayesian formulation 45
4.3 Frequentist analysis 47
4.4 Some more general frequentist developments 50
4.5 Some further Bayesian examples 59
Notes 4 62
5 Interpretations of uncertainty 64
Summary 64
5.1 General remarks 64
5.2 Broad roles of probability 65
5.3 Frequentist interpretation of upper limits 66
5.4 Neyman Pearson operational criteria 68
5.5 Some general aspects of the frequentist approach 68
5.6 Yet more on the frequentist approach 69
5.7 Personalistic probability 71
5.8 Impersonal degree of belief 73
5.9 Reference priors 76
5.10 Temporal coherency 78
5.11 Degree of belief and frequency 79
5.12 Statistical implementation of Bayesian analysis 79
5.13 Model uncertainty 84
5.14 Consistency of data and prior 85
5.15 Relevance of frequentist assessment 85
5.16 Sequential stopping 88
5.17 A simple classification problem 91
Notes 5 93
6 Asymptotic theory 96
Summary 96
6.1 General remarks 96
6.2 Scalar parameter 97
6.3 Multidimensional parameter 107
6.4 Nuisance parameters 109
6.5 Tests and model reduction 114
6.6 Comparative discussion 117
6.7 Profile likelihood as an information summarizer 119
6.8 Constrained estimation 120
6.9 Semi asymptotic arguments 124
6.10 Numerical analytic aspects 125
6.11 Higher order asymptotics 128
Notes 6 130
7 Further aspects of maximum likelihood 133
Summary 133
7.1 Multimodal likelihoods 133
7.2 Irregular form 135
7.3 Singular information matrix 139
7.4 Failure of model 141
7.5 Unusual parameter space 142
7.6 Modified likelihoods 144
Notes 7 159
8 Additional objectives 161
Summary 161
8.1 Prediction 161
8.2 Decision analysis 162
8.3 Point estimation 163
8.4 Non likelihood based methods 169
Notes 8 175
9 Randomization based analysis 178
Summary 178
9.1 General remarks 178
9.2 Sampling a finite population 179
9.3 Design of experiments 184
Notes 9 192
Appendix A: A brief history 194
Appendix B: A personal view 197
References 201
Author index 209
Subject index 213 |
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| spelling | Cox, David R. 1924-2022 Verfasser (DE-588)119013169 aut Principles of statistical inference D. R. Cox 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XV, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilités Statistique mathématique Statistische analyse gtt Mathematical statistics Probabilities Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 s b DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015464185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cox, David R. 1924-2022 Principles of statistical inference Probabilités Statistique mathématique Statistische analyse gtt Mathematical statistics Probabilities Inferenzstatistik (DE-588)4247120-5 gnd |
| subject_GND | (DE-588)4247120-5 |
| title | Principles of statistical inference |
| title_auth | Principles of statistical inference |
| title_exact_search | Principles of statistical inference |
| title_exact_search_txtP | Principles of statistical inference |
| title_full | Principles of statistical inference D. R. Cox |
| title_fullStr | Principles of statistical inference D. R. Cox |
| title_full_unstemmed | Principles of statistical inference D. R. Cox |
| title_short | Principles of statistical inference |
| title_sort | principles of statistical inference |
| topic | Probabilités Statistique mathématique Statistische analyse gtt Mathematical statistics Probabilities Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Probabilités Statistique mathématique Statistische analyse Mathematical statistics Probabilities Inferenzstatistik |
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