The foundations of statistics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Wiley
1954
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| Schriftenreihe: | Wiley Publications in Statistics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 294 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804116373380530176 |
|---|---|
| adam_text | Contents
Postulates of a personalistic theory of decision...................End papers
1. Introduction
1. The role of foundations..................................... 1
2. Historical background............................................ 1
3. General outline of this book........... ......................... 4
2. Preliminary Considerations on Decision in the Face of Uncertainty
1. Introduction......................................................... 6
2. The person.......................................................... 7
3. The world, and states of the world ............................ 8
4. Events.............................................................. 10
5. Consequences, acts, and decisions . ............................. 13
6. The simple ordering of acts with respect to preference .......... 17
7. The sure-thing principle............................................ 21
3. Personal Probability
1. Introduction...................................................... 27
2. Qualitative personal probability 30
3. Quantitative personal probability .................................. 33
4. Some mathematical details........................................... 40
5. Conditional probability, qualitative and quantitative............... 43
6. The approach to certainty through experience........................ 46
7. Symmetric sequences of events....................................... 50
4. Critical Comments on Personal Probability
1. Introduction . . . ................................................ 56
2. Some shortcomings of the personalistic view......................... 57
3. Connection with other views......................................... 60
4. Criticism of other views............................................ 60
5» The role of symmetry in probability................................. 63
6. How can science use a personalistic view of probability? ........... 67
5. Utility
1. Introduction........................................................ 69
2. Gambles............................................................ 70
3. Utility, and preference among gambles............................... 73
4. The extension of utility to more general acts....................... 76
5. Small worlds ....................................................... 82
6. Historical and critical comments on utility ........................ 91
xiii
XIV
CONTENTS
6. Observation
1. Introduction.......................................................105
2. What an observation is.............................................106
3. Multiple observations, and extensions of observations and of sets of
acts.............................................................Ill
4. Dominance and admissibility........................................114
5. Outline of the design of experiments...............................116
7. Partition Problems
1. Introduction.......................................................120
2. Structure of (twofold) partition problems..........................121
3. The value of observation...........................................125
4. Extension of observations, and sufficient statistics...............128
5. Likelihood ratios..................................................134
6. Repeated observations..............................................140
7. Sequential probability ratio procedures............................142
8. Standard form, and absolute comparison between observations . . . 148
8. Statistics Proper
1. Introduction.......................................................154
2. What is statistics proper?.........................................154
3. Multipersonal problems............................................ 154
4. The minimax theory.................................................156
9. Introduction to the Minimax Theory
1. Introduction.......................................................158
2. The behavioralistic outlook........................................159
3. Mixed acts.........................................................162
4. Income and loss....................................................163
5. The minimax rule, and the principle of admissibility...............164
6. Illustrations of the minimax rule..................................165
7. Objectivistie motivation of the minimax rule ......................168
8. Loss as opposed to negative income in the minimax rule ............169
10. A Personaiastic Reinterpretation of the Minimax Theory
1. Introduction.......................................................172
2. A model of group decision..........................................172
3. The group minimax rule, and the group principle of admissibility . 173
4. Critique of the group minimax rule...........................174 11 12
11. The Parallelism between the Minimax Theory and the Theory of
Two-Person Games
1. Introduction........................................................178
2. Standard games .....................................................178
3. Minimax play........................................................180
4. Parallelism and contrast with the minimax theories..................180
12. The Mathematics of Minimax Problems
1. Introduction.......................................................184
2. Abstract games.....................................................184
CONTENTS
XV
3. Bilinear games..................................................186
4. An example of a bilinear game...................................189
5. Bilinear games exhibiting symmetry..............................193
13. Objections to the Minimax Rules
1. Introduction........................................................200
2. A confusion between loss and negative income........................200
3. Utility and the minimax rule........................................201
4. Almost sub-minimax acts.............................................203
5. The minimax rule does not generate a simple ordering................205
14. The Minimax Theory Applied to Observations
1. Introduction........................................................208
2. Recapitulation of partition problems................................208
3. Sufficient statistics...............................................212
4. Simple dichotomy, an example........................................212
5. The approach to certainty...........................................214
6. Cost of observation.................................................214
7. Sequential probability ratio procedures.............................215
8. Randomization ......................................................216
9. Mixed acts in statistics............................................217
f
15. Point Estimation
1. Introduction........................................................220
2. The verbalistic concept of point estimation.........................221
3. Examples of problems of point estimation............................221
4. Criteria that have been proposed for point estimates................223
5. A behavior alistic review of the criteria for point estimation .... 229
6. A behavioralistic review, continued.................................234
7. A behavioralistic review, concluded.................................244
16. Testing
1. Introduction........................................................246
2. A theory of testing.................................................247
3. Testing in practice.................................................252
17. Interval Estimation and Related Topics
1. Estimates of the accuracy of estimates..............................257
2. Interval estimation and confidence intervals........................259
3. Tolerance intervals.................................................262
4. Fiducial probability................................................262
Appendix 1. Expected Value..................................................263
Appendix 2. Convex Functions................................................266
Appendix 3. Bibliographic Material..........................................270
Technical Symbols.............................. ..........................283
Author Index..................................................................285
General Index.................................................................289
|
| any_adam_object | 1 |
| author | Savage, Leonard J. 1917-1971 |
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| author_facet | Savage, Leonard J. 1917-1971 |
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie Wirtschaftswissenschaften |
| format | Book |
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| institution | BVB |
| language | English |
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| physical | XV, 294 S. graph. Darst. |
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| publishDate | 1954 |
| publishDateSearch | 1954 |
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| publisher | Wiley |
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| spelling | Savage, Leonard J. 1917-1971 Verfasser (DE-588)119309882 aut The foundations of statistics Leonard J. Savage New York, NY [u.a.] Wiley 1954 XV, 294 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley Publications in Statistics Statistik (DE-588)4056995-0 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Statistik (DE-588)4056995-0 s Grundlage (DE-588)4158388-7 s 1\p DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260293&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 | Savage, Leonard J. 1917-1971 The foundations of statistics Statistik (DE-588)4056995-0 gnd Grundlage (DE-588)4158388-7 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4158388-7 |
| title | The foundations of statistics |
| title_auth | The foundations of statistics |
| title_exact_search | The foundations of statistics |
| title_full | The foundations of statistics Leonard J. Savage |
| title_fullStr | The foundations of statistics Leonard J. Savage |
| title_full_unstemmed | The foundations of statistics Leonard J. Savage |
| title_short | The foundations of statistics |
| title_sort | the foundations of statistics |
| topic | Statistik (DE-588)4056995-0 gnd Grundlage (DE-588)4158388-7 gnd |
| topic_facet | Statistik Grundlage |
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