Elementary decision theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1970
|
| Ausgabe: | 6. print. |
| Schriftenreihe: | Wiley publications in statistics
A Wiley publication of related interest to statisticians |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 364 S. Illustrationen |
Internformat
MARC
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| 245 | 1 | 0 | |a Elementary decision theory |c Herman Chernoff and Lincoln E. Moses |
| 250 | |a 6. print. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1970 | |
| 300 | |a XV, 364 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804115380486012928 |
|---|---|
| adam_text | Contents
CHAPTER PAGE
1 INTRODUCTION 1
1 Introduction 1
2 An Example 2
3 Principles Used in Decision Making .... 9
4 Summary 10
2 DATA PROCESSING 17
1 Introduction 17
2 Data Representation 17
3 Graphical Representations: Histogram .... 20
4 Graphical Representations: Cumulative Frequency
Polygon 23
5 Descriptive Measures: Summation 29
6 Descriptive Measures: Sample Mean and
Variance 33
f7 Simplified Computation Scheme for sample Mean
and Standard Deviation Using Grouped Data . . 38
8 Summary 40
3 INTRODUCTION TO PROBABILITY AND RANDOM VARIABLES . . 41
1 Introduction 41
2 Two Examples 41
3 Probability Distributions and Cumulative
Distribution Functions 46
4 Probability Density Function—Discrete Case . . 54
5 Probability Density Function—Continuous Case . . 56
f6 Population and Random Samples 59
7 The Normal Population 62
xi
xii CONTENTS
CHAPTEB PAGE
8 Sets and Functions 68
9 Review of Probability 73
4 UTILITY AND DESCRIPITIVE STATISTICS 79
1 Introduction 79
2 Utility 79
f2.1 The Assumptions Behind Utility ... 81
2.2 Application of Utility 86
3 Probability and Expectation . . ... . .89
f4 Application of Utility to Fair Bets 99
f5 The St. Petersburg Paradox 104
6 Descriptive Parameters 106
7 The Mean and Variance 114
7.1 Some Properties of the Mean, Variance, and
Standard Deviation 114
8 Summary 117
5 UNCERTAINTY DUE TO IGNOBANCE OF THE
STATE OF NATURE 119
1 Introduction 119
2 Two States of Nature—an Example .... 119
3 Two States of Nature: Convex Sets and Lines . . 127
4 Two States of Nature: Bayes Strategies and
Supporting Lines 136
5 Two States of Nature: Minimax Strategies . . . 147
6 Two States of Nature: Regret 150
7 Lines, Planes, And Convex Sets in Higher
Dimensions 155
8 Three or More Unknown States of Nature . . . 159
9 Summary 163
6 THE COMPUTATION OF BAYES STRATEGIES 166
1 A Posteriori Probability and the No Data
Problem 166
2 Conditional Probability 170
3 A Posteriori Probability 174
4 Computation of Bayes Strategies 179
4.1 Remarks 180
5 Independence 183
CONTENTS xiii
CHAPTER PAGE
6 Summary 190
7 Review at the End of Chapter 6 192
7 INTBODTTCTION TO CLASSICAL STATISTICS 195
1 Introduction 195
2 An Example of Hypothesis Testing .... 195
2.1 Bayes Strategies 200
2.2 The Name Testing Hypotheses . . .202
2.3 Another Example 204
3 Estimation 207
4 Confidence Intervals 214
f5 Significance Testing 217
f 6 A Decision Making Problem Where Common Statisti¬
cal Procedures Do Not Apply 221
7 Summary 225
8 models 228
1 Introduction 228
2 Models of Probability and Utility 230
3 Models of the Set of Available Actions .... 231
4 Models of Sets of Possible States of Nature . . .233
5 Models of Regret Functions 234
6 Models of Experiments 235
f6.1 Specifications of Distributions . . . . 236
f 6.2 Models Concerned with Relations
Between Variables 238
7 Models of the Set of Available Strategies . . .240
8 The Models for the Problems of Testing and
Estimation 242
9 Summary 243
9 TESTING HYPOTHESES 245
1 Introduction 245
2 Notation 245
3 Simple Hypothesis Versus Simple Hypothesis
(Two States of Nature) 246
4 Composite Hypotheses Involving One Parameter . . 255
5 Composite Hypotheses Involving One Parameter:
Two Tailed Tests 258
Xiv CONTENTS
CHAPTER PAGE
6 Several Parameters . 262
7 Design of Experiments 264
8 Sequential Analysis 266
f8.1 Details in the Binomial Example . . . 269
f8.2 Details in the Normal Example with
Known Variance 271
9 Summary 272
10 ESTIMATION AND CONFIDENCE INTEHVALS 275
1 Introduction 275
2 Formal Structure of the Estimation Problem:
One Parameter Case 275
3 Methods of Estimation 277
3.1 The Analogue Method or Method of Moments 277
3.2 The Maximum Likelihood Method . . .278
3.3 Bayes Strategies 280
3.4 Convenience of the Various Methods of
Estimation 282
4 Large Sample Properties of Estimators .... 283
5 Small Sample Properties of Estimators .... 287
5.1 Invariance Under Transformation of
Parameter 287
5.2 Unbiased Estimators 288
f5.3 Sufficiency 290
6 Several Parameters 291
7 Confidence Intervals: Large Samples .... 292
8 Confidence Intervals: Small Samples .... 293
9 Summary 295
APPENDIX
A NOTATION 298
B MATHEMATICAL TABLES 302
Bx Short Table of Squares and Square Roots . . 302
B2 Logarithms 303
C TABLES OF RANDOM DEVIATES 305
Cj. Table of Random Digits 305
C2 Table of Random Normal Deviates . . . 306
CONTENTS XV
CHAPTER PAGE
D TABLES OF PROBABILITY DISTRIBUTIONS 307
Dj Areas Under the Normal Curve From i + ao to oo 307
D2 Chi Square Distribution 308
D3 Exponential Distribution 309
D4 Student s t Distribution 310
E DERIVATIONS 311
E± Derivation of an Equation for the Sample Variance 311
E2 Simplified Computation Scheme for the Sample
Mean and Variance Using Grouped Data . . 312
E3 Axioms of Probability 313
E4 Properties of Expectation 315
E5 The Convex Set Generated by A is the Set of
Weighted Averages of Elements of A . . 321
E6 Relevance of Risks 323
E7 Probabilities of Compound Sets .... 325
Es Bayes Strategies Obtained by Using A Posteriori
Probabilities 327
E9 Crossing Bridges One at a Time .... 329
E10 Mean and Variance of X 330
Elx For Testing a Simple Hypothesis Versus a Simple
Alternative, the Bayes Strategies are Likelihood
Ratio Tests 332
E12 Some Likelihood Ratio Tests 335
E13 Admissibility of the Two State Likelihood Ratio
Tests for Certain Problems Involving Composite
Hypotheses 338
E14 Sequential Likelihood Ratio Tests . . . .340
E1B Some Sequential Likelihood Ratio Tests . . 344
F MISCELLANEOUS REMARKS ABOUT GAME THEORY AND
UTILITY THEORY 346
Ft Remarks About Game Theory 346
F2 Outline of the Derivation of the Utility Function 350
PARTIAL LIST OF ANSWERS TO EXERCISES 353
INDEX 359
|
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| author | Chernoff, Herman 1923- Moses, Lincoln E. 1921-2006 |
| author_GND | (DE-588)139425640 (DE-588)12422721X |
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| bvnumber | BV000950355 |
| classification_rvk | QH 233 SK 830 CM 5500 |
| ctrlnum | (OCoLC)256171316 (DE-599)BVBBV000950355 |
| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 6. print. |
| format | Book |
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| language | English |
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| physical | XV, 364 S. Illustrationen |
| publishDate | 1970 |
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| series2 | Wiley publications in statistics A Wiley publication of related interest to statisticians |
| spelling | Chernoff, Herman 1923- Verfasser (DE-588)139425640 aut Elementary decision theory Herman Chernoff and Lincoln E. Moses 6. print. New York [u.a.] Wiley 1970 XV, 364 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Wiley publications in statistics A Wiley publication of related interest to statisticians Statistik (DE-588)4056995-0 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s Entscheidungstheorie (DE-588)4138606-1 s 1\p DE-604 DE-604 Moses, Lincoln E. 1921-2006 Verfasser (DE-588)12422721X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000579861&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 | Chernoff, Herman 1923- Moses, Lincoln E. 1921-2006 Elementary decision theory Statistik (DE-588)4056995-0 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4138606-1 (DE-588)4151278-9 |
| title | Elementary decision theory |
| title_auth | Elementary decision theory |
| title_exact_search | Elementary decision theory |
| title_full | Elementary decision theory Herman Chernoff and Lincoln E. Moses |
| title_fullStr | Elementary decision theory Herman Chernoff and Lincoln E. Moses |
| title_full_unstemmed | Elementary decision theory Herman Chernoff and Lincoln E. Moses |
| title_short | Elementary decision theory |
| title_sort | elementary decision theory |
| topic | Statistik (DE-588)4056995-0 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Statistik Entscheidungstheorie Einführung |
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