A mathematical theory of evidence:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton Univ. Press
1976
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 297 S. graph. Darst. |
| ISBN: | 0691081751 069110042X 9780691100425 |
Internformat
MARC
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| 245 | 1 | 0 | |a A mathematical theory of evidence |c Glenn Shafer |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 1976 | |
| 300 | |a XIII, 297 S. |b graph. Darst. | ||
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| 650 | 7 | |a Probabilidade e estatistica |2 larpcal | |
| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 4 | |a Evidence | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Probabilities | |
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Datensatz im Suchindex
| _version_ | 1804116416840859648 |
|---|---|
| adam_text | CONTENTS
FOREWORD by A. P. Dempster vii
PREFACE ix
CHAPTER 1. INTRODUCTION 3
§1. Synopsis 4
§2. The Idea of Chance 9
§3. The Doctrine of Chances 12
§4. Chances as Degrees of Belief 16
§5. The Bayesian Theory of Partial Belief 18
§6. The Role of Judgment 20
§7. The Representation of Ignorance 22
§8. Combination vs. Conditioning 25
§9. The Representation of Probable Reasoning 28
§10. Statistical Inference 29
§11. The Bayesian Theory as a Limiting Case 32
§12. Probability 33
CHAPTER 2. DEGREES OF BELIEF 35
§1. Subsets as Propositions 35
§2. Basic Probability Numbers 37
§3. Belief Functions 39
§4. Commonality Numbers 40
§5. Degrees of Doubt and Upper Probabilities 42
§6. Bayesian Belief Functions 44
§7. Mathematical Appendix 46
CHAPTER 3. DEMPSTER S RULE OF COMBINATION 57
§1. Combining Two Belief Functions 58
§2. Multiplying Commonality Numbers 61
§3. Combining Several Belief Functions 62
§4. The Weight of Conflict 64
§5. Conditioning Belief Functions 66
§6. Other Properties of Dempster s Rule 67
§7. Mathematical Appendix 68
xi
Xii CONTENTS
CHAPTER 4. SIMPLE AND SEPARABLE SUPPORT FUNCTIONS 74
§1. Simple Support Functions 75
§2. Bernoulli s Rule of Combination 75
§3. The Weight of Evidence 77
§4. Heterogeneous Evidence 79
§5. Conflicting Evidence 82
§6. Separable Support Functions g6
CHAPTER 5. THE WEIGHTS OF EVIDENCE 88
§1. Decomposing Separable Support Functions 89
§2. Combining Weights of Evidence 90
§3. The Assessment of Evidence 93
§4. The Weight of Internal Conflict 95
§5. The Impingement Function 97
§6. The Weight of Conflict Conjecture 98
§7. Some Numerical Examples 100
§8. Mathematical Appendix 103
CHAPTER 6. COMPATIBLE FRAMES OF DISCERNMENT 114
§1. Refinements and Coarsenings 115
§2. The Inner and Outer Reductions 117
§3. Is There an Ultimate Refinement? 119
§4. Families of Compatible Frames 121
§5. Consistent Belief Functions 125
§6. Independent Frames 127
§7. Mathematical Appendix 129
CHAPTER 7. SUPPORT FUNCTIONS 141
§1. The Class of Support Functions 142
§2. Support, Dubiety, and Plausibility 144
§3. The Vacuous Extension of a Support Function 146
§4. Evidential Independence 147
§5. Cognitive Independence 149
§6. Mathematical Appendix 152
CHAPTER 8. THE DISCERNMENT OF EVIDENCE 172
§1. Families of Compatible Support Functions 173
§2. Discerning the Interaction of Evidence 175
§3. Discerning Weights of Evidence I82
§4. If the Weight of Conflict Conjecture is True 185
§5. Mathematical Appendix 186
CONTENTS xiii
CHAPTER 9. QUASI SUPPORT FUNCTIONS lg6
§1. Infinite Contradictory Evidence ig7
§2. The Class of Quasi Support Functions I99
§3. Chances are not Degrees of Support 201
§4. The Bayesian Profusion of Infinite Weights 202
§5. Bayes Theorem 204
§6. Mathematical Appendix 209
CHAPTER 10. CONSONANCE 219
§1. Consonant Support Functions 219
§2. The Contour Function 221
§3. The Embarrassment of Dissonance 223
§4. Inferential Evidence 226
§5. Mathematical Appendix 229
CHAPTER 11. STATISTICAL EVIDENCE 237
§1. A Convention for Assessing Statistical Evidence 238
§2. The Weights of Evidence 245
§3. Epistemic vs. Aleatory Combination 247
§4. The Effect of a Bayesian Prior 250
§5. Discounting Statistical Evidence 251
§6. Specifications on Compatible Frames 255
§7. The Role of Supposition 258
§8. Perspective 262
§9. Mathematical Appendix 264
CHAPTER 12. THE DUAL NATURE OF PROBABLE REASONING 274
§1. The Effect of Assumptions 274
§2. The Need for Assumptions 276
§3. Choosing our Frames of Discernment 279
§4. The Role of Epistemic Probability 284
§5. Two Tasks 285
BIBLIOGRAPHY 287
INDEX 292
|
| any_adam_object | 1 |
| author | Shafer, Glenn 1946- |
| author_GND | (DE-588)131924060 |
| author_facet | Shafer, Glenn 1946- |
| author_role | aut |
| author_sort | Shafer, Glenn 1946- |
| author_variant | g s gs |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA273 |
| callnumber-search | QA273 |
| callnumber-sort | QA 3273 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 SG 700 SK 800 SK 830 |
| ctrlnum | (OCoLC)1859710 (DE-599)BVBBV001972781 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:10Z |
| institution | BVB |
| isbn | 0691081751 069110042X 9780691100425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001286672 |
| oclc_num | 1859710 |
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| physical | XIII, 297 S. graph. Darst. |
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| publisher | Princeton Univ. Press |
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| spelling | Shafer, Glenn 1946- Verfasser (DE-588)131924060 aut A mathematical theory of evidence Glenn Shafer Princeton, NJ [u.a.] Princeton Univ. Press 1976 XIII, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bewijstheorie gtt Probabilidade e estatistica larpcal Probabilités Statistique mathématique Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie (DE-588)4395834-5 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 s Statistik (DE-588)4056995-0 s DE-604 Dempster-Shafer-Theorie (DE-588)4395834-5 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001286672&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 | Shafer, Glenn 1946- A mathematical theory of evidence Bewijstheorie gtt Probabilidade e estatistica larpcal Probabilités Statistique mathématique Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie (DE-588)4395834-5 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4395834-5 (DE-588)4137007-7 (DE-588)4064324-4 (DE-588)4056995-0 |
| title | A mathematical theory of evidence |
| title_auth | A mathematical theory of evidence |
| title_exact_search | A mathematical theory of evidence |
| title_full | A mathematical theory of evidence Glenn Shafer |
| title_fullStr | A mathematical theory of evidence Glenn Shafer |
| title_full_unstemmed | A mathematical theory of evidence Glenn Shafer |
| title_short | A mathematical theory of evidence |
| title_sort | a mathematical theory of evidence |
| topic | Bewijstheorie gtt Probabilidade e estatistica larpcal Probabilités Statistique mathématique Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie (DE-588)4395834-5 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Bewijstheorie Probabilidade e estatistica Probabilités Statistique mathématique Evidence Mathematical statistics Probabilities Dempster-Shafer-Theorie Wahrscheinlichkeit Wahrscheinlichkeitsrechnung Statistik |
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