Choice against chance: an introduction to statistical decision theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1970
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| Schriftenreihe: | Addison-Wesley series in behavioral science: quantitative methods
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 284 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Choice against chance |b an introduction to statistical decision theory |c John Aitchison |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1970 | |
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Datensatz im Suchindex
| _version_ | 1804117250536374272 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Problems of Decision Making under Uncertainty
1.1 Introduction 1
1.2 Preferences and uncertainties 3
1.3 Some challenging problems 6
1.4 Business decisions 7
1.5 Classification problems 8
1.6 Sampling inspection of quality 12
1.7 Estimation 13
1.8 Treatment selection 15
1.9 Negotiating contracts and tariffs 17
1.10 The problem of control 18
Chapter 2 The Language of Uncertainty: Basic Grammar
2.1 The pervasiveness of uncertainty 21
2.2 Model building 23
2.3 The feature of stability 26
2.4 Record set 28
2.5 Events and records 30
2.6 Simple properties of relative frequency 33
2.7 Requirements of a probability model 35
2.8 Specification of a probability model 36
2.9 Examples of probability models 37
Chapter 3 The Language of Uncertainty: Towards Fluency
3.1 Models for compound experiments 42
3.2 Unrelated or independent experiments 43
r/7
viii Contents
3.3 Sequential experiments 50
3.4 Experiments with two dimensional records 58
3.5 Induced experiments 65
3.6 Binomial trials 72
3.7 Average and expectation 76
3.8 A measure of spread 82
3.9 Properties of mean and variance 85
3.10 A probability glossary 90
Chapter 4 Models for Competitive Behavior
4.1 An illustrative game 92
4.2 Structure of a two person game 95
4.3 Introduction of a new product formulated as a game 96
4.4 Simple and randomized strategies 98
4.5 Randomized strategy of opponent known to player: Bayesian strategies 100
4.6 Graphic representation of the analysis 105
4.7 Admissible and inadmissible strategies 108
4.8 Admissibility of Bayesian strategies 110
4.9 Randomized strategy of opponent unknown to player 112
4.10 The case of the pessimistic player (max min) 113
4.11 The max min approach to introducing a new product 117
Chapter 5 The Nature of Statistical Inference
5.1 The class of possible probability models 119
5.2 Measures of plausibility 123
5.3 Plausibilities before and after experimentation 124
5.4 Plausibility analysis of cell estimation problem 131
5.5 Plausibility analysis of binomial trials 133
5.6 Plausible prediction 134
5.7 Difficulties of plausibility analysis 138
5.8 Hypothesis testing 139
5.9 Estimation 143
5.10 Minimum variance unbiased estimator 148
5.11 Maximum likelihood estimates 152
Chapter 6 The Structure of Statistical Decision Theory
6.1 The basic ingredients 155
6.2 The assessment of procedures 160
6.3 Admissible and inadmissible procedures 162
6.4 The structure of the decision problem 167
6.5 The introduction of additional information 171
6.6 Some comments on mathematics and philosophy 174
6.7 The construction of a Bayesian procedure 175
6.8 Statistical decision making as a game 181
Contents ix
6.9 The rational man concept 182
6.10 Graphic investigation 183
6.11 Design or choice of experiment 185
6.12 Utility dependent on the outcome of the informative experiment . . 191
6.13 General utility structure dependent on action, state of nature, outcome
observed, and experiment undertaken 196
Chapter 7 Applications and Extensions of Statistical Decision Theory
7.1 Decision trees 202
7.2 Loss structures 213
7.3 Relation of decision theory to statistical inference 214
7.4 Utility function involving a prediction assessment: prognosis analysis 217
7.5 Application to the negotiation of a wage structure 222
7.6 Application to the replacement problem 225
7.7 Applications to the choice of treatment 228
7.8 Application to selecting a quality improver 230
7.9 Sequential decision making: construction of a stopping rule . . . 232
7.10 A problem of process control 239
7.11 Sequential statistical decision making 244
Chapter 8 History, Present Extensions, and Future Trends
8.1 A brief history 249
8.2 Recapitulation 254
8.3 Extensions 258
8.4 Relation to other disciplines 259
8.5 Future trends 263
Further Reading 265
Appendices
1. Functions 269
2. Summation Instructions 270
3. Max and Min Instructions 271
4. Weighted Averages 272
Index 277
|
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| indexdate | 2024-07-09T15:51:25Z |
| institution | BVB |
| language | English |
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| spelling | Aitchison, John 1788-1875 Verfasser (DE-588)11928748X aut Choice against chance an introduction to statistical decision theory John Aitchison Reading, Mass. [u.a.] Addison-Wesley 1970 IX, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in behavioral science: quantitative methods Toma de decisiones - Métodos estadísticos Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aitchison, John 1788-1875 Choice against chance an introduction to statistical decision theory Toma de decisiones - Métodos estadísticos Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| subject_GND | (DE-588)4077850-2 |
| title | Choice against chance an introduction to statistical decision theory |
| title_auth | Choice against chance an introduction to statistical decision theory |
| title_exact_search | Choice against chance an introduction to statistical decision theory |
| title_full | Choice against chance an introduction to statistical decision theory John Aitchison |
| title_fullStr | Choice against chance an introduction to statistical decision theory John Aitchison |
| title_full_unstemmed | Choice against chance an introduction to statistical decision theory John Aitchison |
| title_short | Choice against chance |
| title_sort | choice against chance an introduction to statistical decision theory |
| title_sub | an introduction to statistical decision theory |
| topic | Toma de decisiones - Métodos estadísticos Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| topic_facet | Toma de decisiones - Métodos estadísticos Statistische Entscheidungstheorie |
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