Statistical reasoning with imprecise probabilities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Chapman and Hall
1991
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
42 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 706 S. |
| ISBN: | 0412286602 |
Internformat
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| 245 | 1 | 0 | |a Statistical reasoning with imprecise probabilities |c Peter Walley |
| 250 | |a 1. ed. | ||
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| 300 | |a XII, 706 S. | ||
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Datensatz im Suchindex
| _version_ | 1824294525521100800 |
|---|---|
| adam_text |
Contents
Preface ix
1 Reasoning and behaviour 1
1.1 Introduction 1
1.2 Outline of the book 9
1.3 Interpretations of probability 13
1.4 Beliefs and behaviour 17
1.5 Inference and decision 21
1.6 Reasoning and rationality 26
1.7 Assessment strategies 32
1.8 Survey of related work 42
2 Coherent previsions 52
2.1 Possibility 54
2.2 Probability currency 58
2.3 Upper and lower previsions 61
2.4 Avoiding sure loss 67
2.5 Coherence 72
2.6 Basic properties of coherent previsions 76
2.7 Coherent probabilities 81
2.8 Linear previsions and additive probabilities 86
2.9 Examples of coherent previsions 92
2.10 Interpretations of lower previsions 101
2.11 Objections to behavioural theories of probability 109
3 Extensions, envelopes and decisions 120
3.1 Natural extension 121
3.2 Extension from a field 127
3.3 Lower envelopes of linear previsions 132
3.4 Linear extension 136
3.5 Invariant linear previsions 139
3.6 Compactness and extreme points of Jl(P) 145
vi CONTENTS
3.7 Desirability and preference 150
3.8 Equivalent models for beliefs 156
3.9 Decision making 160
4 Assessment and elicitation 167
4.1 A general elicitation procedure 168
4.2 Finitely generated models and simplex representations 174
4.3 Steps in the assessment process 177
4.4 Classificatory probability 188
4.5 Comparative probability 191
4.6 Other types of assessment 197
5 The importance of imprecision 207
5.1 Uncertainty, indeterminacy and imprecision 209
5.2 Sources of imprecision 212
5.3 Information from Bernoulli trials 217
5.4 Prior data conflict 222
5.5 Bayesian noninformative priors 226
5.6 Indecision 235
5.7 Axioms of precision 241
5.8 Practical reasons for precision 248
5.9 Bayesian sensitivity analysis 253
5.10 Second order probabilities 258
5.11 Fuzzy sets 261
5.12 Maximum entropy 266
5.13 The Dempster Shafer theory of belief functions 272
6 Conditional previsions 282
6.1 Updated and contingent previsions 284
6.2 Separate coherence 289
6.3 Coherence with unconditional previsions 293
6.4 The generalized Bayes rule 297
6.5 Coherence axioms 301
6.6 Examples of conditional previsions 308
6.7 Extension of conditional and marginal previsions 313
6.8 Conglomerability 317
6.9 Countable additivity 323
6.10 Conditioning on events of probability zero 328
6.11 Updating beliefs 334
7 Coherent statistical models 341
7.1 General concepts of coherence 342
7.2 Sampling models 349
CONTENTS vii
7.3 Coherence of sampling model and posterior previsions 362
7.4 Inferences from improper priors 367
7.5 Confidence intervals and relevant subsets 377
7.6 Proper prior previsions 388
7.7 Standard Bayesian inference 393
7.8 Inferences from imprecise priors 397
7.9 Joint prior previsions 403
8 Statistical reasoning 406
8.1 A general theory of natural extension 408
8.2 Extension to prior previsions 415
8.3 Extension to predictive previsions 421
8.4 Extension to posterior previsions 424
8.5 Posteriors for imprecise sampling models 430
8.6 The likelihood principle 434
9 Structural judgements 442
9.1 Independent events 443
9.2 Independent experiments 448
9.3 Constructing joint previsions from independent marginals 452
9.4 Permutability 457
9.5 Exchangeability 460
9.6 Robust Bernoulli models 467
9.7 Structural judgements 472
Notes 478
Chapter 1 478
Chapter 2 490
Chapter 3 502
Chapter 4 509
Chapter 5 519
Chapter 6 545
Chapter 7 561
Chapter 8 576
Chapter 9 595
Appendices
A. Verifying coherence 596
B. M Coherence 599
C. Win and place betting on horses 602
D. Topological structure of if and 608
E. Separating hyperplane theorems 611 |
| any_adam_object | 1 |
| author | Walley, Peter |
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| ctrlnum | (OCoLC)260148433 (DE-599)BVBBV004412139 |
| dewey-full | 519.5 519.520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 519.5 20 |
| dewey-search | 519.5 519.5 20 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV004412139 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-17T09:00:33Z |
| institution | BVB |
| isbn | 0412286602 |
| language | English |
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| physical | XII, 706 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Chapman and Hall |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Walley, Peter Verfasser aut Statistical reasoning with imprecise probabilities Peter Walley 1. ed. London u.a. Chapman and Hall 1991 XII, 706 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 42 Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Mathematical statistics Probabilities Stochastische Unschärfe (DE-588)4183381-8 gnd rswk-swf Partielle Information (DE-588)4232570-5 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Stochastische Unschärfe (DE-588)4183381-8 s DE-604 Statistische Schlussweise (DE-588)4182963-3 s Partielle Information (DE-588)4232570-5 s Monographs on statistics and applied probability 42 (DE-604)BV002494005 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002737249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walley, Peter Statistical reasoning with imprecise probabilities Monographs on statistics and applied probability Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Mathematical statistics Probabilities Stochastische Unschärfe (DE-588)4183381-8 gnd Partielle Information (DE-588)4232570-5 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4183381-8 (DE-588)4232570-5 (DE-588)4182963-3 |
| title | Statistical reasoning with imprecise probabilities |
| title_auth | Statistical reasoning with imprecise probabilities |
| title_exact_search | Statistical reasoning with imprecise probabilities |
| title_full | Statistical reasoning with imprecise probabilities Peter Walley |
| title_fullStr | Statistical reasoning with imprecise probabilities Peter Walley |
| title_full_unstemmed | Statistical reasoning with imprecise probabilities Peter Walley |
| title_short | Statistical reasoning with imprecise probabilities |
| title_sort | statistical reasoning with imprecise probabilities |
| topic | Probabilités Statistiek gtt Statistique mathématique Waarschijnlijkheid (statistiek) gtt Statistik Mathematical statistics Probabilities Stochastische Unschärfe (DE-588)4183381-8 gnd Partielle Information (DE-588)4232570-5 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Probabilités Statistiek Statistique mathématique Waarschijnlijkheid (statistiek) Statistik Mathematical statistics Probabilities Stochastische Unschärfe Partielle Information Statistische Schlussweise |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002737249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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