The likelihood principle:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hayward, Calif.
1988
|
| Edition: | 2. ed. |
| Series: | Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series
6. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 143 - 160.2 |
| Physical Description: | XII, 208 S. |
| ISBN: | 0940600137 |
Staff View
MARC
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| 245 | 1 | 0 | |a The likelihood principle |c James O. Berger ; Robert L. Wolpert |
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Record in the Search Index
| _version_ | 1804123992976523264 |
|---|---|
| adam_text | Titel: The likelihood principle
Autor: Berger, James O
Jahr: 1988
TABLE OF CONTENTS CHAPTER 1. INTRODUCTION ......................... 1 CHAPTER 2. CONDITIONING ......................... 5 2.1. Simple Examples ......................... 5 2.2. Relevant Subsets ........................ 11 2.3. Ancillarity...........................13 2.4. Conditional Frequenti st Procedures ............... 14 2.4.1. Conditional Confidence ................. 14 2.4.2. Estimated Confidence .................. 16 2.5. Criticisms of Partial Conditioning ............... 16 CHAPTER 3. THE LIKELIHOOD PRINCIPLE AND GENERALIZATIONS ......... 19 3.1. Introduction..........................19 3.2. History of the Likelihood Principle ............... 22 3.3. Birnbaum s Development - the Discrete Case...........24 3.3.1. Evidence , Conditionality, and Sufficiency ........ 24 3.3.2. Axiomatic Development .................. 26 3.4. Generalizations Beyond the Discrete Case ............ 28 3.4.1. Difficulties in the Nondiscrete Case ..........29 3.4.2. Evidence, Conditionality, and Sufficiency ........ 31 3.4.3. The Relative Likelihood Principle ............ 32 3.5. Prediction, Design, Nuisance Parameters, and the LP ....... 36 3.5.1. Introduction ...................... 36 3.5.2. Unobserved Variables: Prediction and Design ...... 37 3.5.3. Nuisance Variables and Parameters ............ 41 x
TABLE OF CONTENTS xi 3.6. Criticisms of Birnbaum s Axiomatic Development ......... 42 3.6.1. The Model Assumption .................. 43 3.6.2. The Evidence Assumption ................. 45 3.6.3. The Weak Conditionality Principle ............ 45 3.6.4. The Sufficiency Principle ................ 46 3.7. Violation of the Likelihood Principle: Inadmissibility and Incoherency...........................50 3.7.1. Introduction ...................... 50 3.7.2. Decision Theoretic Evaluation .............. 52 3.7.3. Betting Evaluation ................... 59 CHAPTER 4. CONSEQUENCES AND CRITICISMS OF THE LIKELIHOOD PRINCIPLE AND THE RELATIVE LIKELIHOOD PRINCIPLE ................. 65 4.1. Incompatibility with Frequentist Concepts ............ 65 4.1.1. Introduction ...................... 65 4.1.2. Objectivity ....................... 67 4.1.3. Procedures for Nonspeaialists .............. 68 4.1.4. Repeatability ...................... 70 4.1.5. The Confidence Principle ................ 71 4.2. The Irrelevance of Stopping Rules................74 4.2.1. Introduction ...................... 74 4.2.2. The (Discrete) Stopping Rule Principle ......... 75 4.3.2. Positive Implications . . ................ 77 4.2.4. Criticisms ....................... 80 4.2.5. Stopping Rules and Inadmissibility ........... 83 4.2.6. The General Stopping Rule Principle ........... 86 4.2.7. Informative Stopping Rules ............... 88 4.3. The Irrelevance of Censoring Mechanisms 4.3.1. Introduction ...................... 90 4.3.2. Fixed Censoring and Equivalent Censoring Mechanisms ... 92 4.3.3. Random Censoring .................... 95 4.3.4. Informative Censoring ................... 103
TABLE OF CONTENTS xii 4.4. Significance Testing ..................... 104 4.4.1. Conflict with the Likelihood Principle ........ 104 4.4.2. Averaging Over More Extreme Observations ...... 105 4.4.3. Testing a Single Null Model ............. 109 4.4.4. Conclusions ..................... 109.3 4.5. Randomization Analysis .................... 110 4.5.1. Introduction ..................... 110 4.5.2. Finite Population Sampling .............. 112 4.5.3. Randomization Tests ................. 117 CHAPTER 5. IMPLEMENTATION OF THE LIKELIHOOD PRINCIPLE ......... 121 5.1. Introduction................ 121 5.2. Non-Bayesian Likelihood Methods ............... 122 5.3. Arguments for Bayesian Implementation ............ 124 5.3.1. General Considerations ................ 124 5.3.2. The Fraser-Monette-Ng , Stone, and Stein Examples . . . 127 5.4. Robust Bayesian Analysis ......... 136 5.5. Conclusions......................... 141 REFERENCES............................... 143 ADDITIONAL OR UPDATED REFERENCES .................... 160 DISCUSSION BY M. J. BAYARRI AND M. H. DEGR00T.............160.3 DISCUSSION BY BRUCE HILL........................ 161 DISCUSSION BY DAVID LANE........................ 175 DISCUSSION BY LUCIEN LE CAM............ .......... 182 REPLY TO THE DISCUSSION........................ 186 ADDITIONAL REFERENCES IN THE DISCUSSION ................ 198 INDEX OF EXAMPLES........................... 200 AUTHOR INDEX .............................. 201 SUBJECT INDEX ............................. 204 ERRATA AND CLARIFICATIONS ....................... 207
|
| any_adam_object | 1 |
| author | Berger, James O. Wolpert, Robert L. |
| author_facet | Berger, James O. Wolpert, Robert L. |
| author_role | aut aut |
| author_sort | Berger, James O. |
| author_variant | j o b jo job r l w rl rlw |
| building | Verbundindex |
| bvnumber | BV009650567 |
| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)18330253 (DE-599)BVBBV009650567 |
| dewey-full | 519.5/44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/44 |
| dewey-search | 519.5/44 |
| dewey-sort | 3519.5 244 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009650567 |
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| indexdate | 2024-07-09T17:38:35Z |
| institution | BVB |
| isbn | 0940600137 |
| language | English |
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| physical | XII, 208 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
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| series | Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series |
| series2 | Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series |
| spelling | Berger, James O. Verfasser aut The likelihood principle James O. Berger ; Robert L. Wolpert 2. ed. Hayward, Calif. 1988 XII, 208 S. txt rdacontent n rdamedia nc rdacarrier Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series 6. Literaturverz. S. 143 - 160.2 Statistique mathématique Waarschijnlijkheid (statistiek) gtt Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf Likelihood-Funktion (DE-588)4657256-9 gnd rswk-swf Likelihood-Funktion (DE-588)4657256-9 s DE-604 Maximum-Likelihood-Schätzung (DE-588)4194624-8 s 1\p DE-604 Wolpert, Robert L. Verfasser aut Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series 6. (DE-604)BV008930051 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006380340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berger, James O. Wolpert, Robert L. The likelihood principle Institute of Mathematical Statistics <Hayward, Calif.>: Lecture notes, monograph series Statistique mathématique Waarschijnlijkheid (statistiek) gtt Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd Likelihood-Funktion (DE-588)4657256-9 gnd |
| subject_GND | (DE-588)4194624-8 (DE-588)4657256-9 |
| title | The likelihood principle |
| title_auth | The likelihood principle |
| title_exact_search | The likelihood principle |
| title_full | The likelihood principle James O. Berger ; Robert L. Wolpert |
| title_fullStr | The likelihood principle James O. Berger ; Robert L. Wolpert |
| title_full_unstemmed | The likelihood principle James O. Berger ; Robert L. Wolpert |
| title_short | The likelihood principle |
| title_sort | the likelihood principle |
| topic | Statistique mathématique Waarschijnlijkheid (statistiek) gtt Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd Likelihood-Funktion (DE-588)4657256-9 gnd |
| topic_facet | Statistique mathématique Waarschijnlijkheid (statistiek) Estimation theory Mathematical statistics Probabilities Maximum-Likelihood-Schätzung Likelihood-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006380340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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