Elements of decision theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Macmillan [u.a.]
1971
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 292 S. Illustrationen |
Internformat
MARC
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| 245 | 1 | 0 | |a Elements of decision theory |c B. W. Lindgren |
| 264 | 1 | |a New York |b Macmillan [u.a.] |c 1971 | |
| 300 | |a XII, 292 S. |b Illustrationen | ||
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Datensatz im Suchindex
| _version_ | 1804116378747142144 |
|---|---|
| adam_text | Contents
Chapter X Preliminaries 1
1.1 Discrete Random Variables 4
1.2 Expected Value 12
1.3 Lines in the Cartesian Plane 17
1.4 Convex Sets 24
Chapter 2 Utility 31
2.1 Preference Axioms 32
2.2 Coding Intermediate Prospects 37
2.3 Utility for Arbitrary Prospects 41
2.4 Utility for Money 48
2.5 Bets, Fair and Unfair 54
2.6 Subjective Probability 60
Chapter 3 No Data Decision Problems 65
3.1 The Set of Mixed Actions 66
3.2 Regret 70
ix
x Contents
3.3 The Minimax Principle 73
3.4 Bayes Solutions 80
3.5 Dominance and Admissibility 88
3.6 Bayes Versus Minimax 90
Chapter 4 Using Data in Making Decisions 98
4.1 Data and the State of Nature 98
4.2 Decision Functions 100
4.3 The Risk Function 102
4.4 Selecting a Decision Function 107
4.5 Conditional Probability 112
4.6 The Posterior Distribution 118
4.7 Successive Observations 120
4.8 Bayes Actions from Posterior Probabilities 123
4.9 Sufficiency 128
Chapter 5 Testing and Estimation 136
5.1 The Estimation Problem 136
5.2 Continuous Distributions 140
5.3 Estimators Using Data 146
5.4 Maximum Likelihood Estimation 151
5.5 Mean Squared Error—Variance 152
5.6 The Problem of Testing Hypotheses 156
5.7 Simple Ho Versus Simple Hx 159
5.8 Composite Hypotheses 165
5.9 Decision Versus Inference 171
Chapter 6 Normal Distributions 174
6.1 Normal Densities 174
6.2 Completing the Square 177
Contents xi
6.3 Sampling from a Normal Population 179
6.4 Posterior Probabilities 181
6.5 The Distribution of X 184
6.6 Tests of Hypotheses About /j. 186
6.7 Confidence Intervals and Probability Intervals 190
Chapter 7 The Bernoulli Model 194
7.1 Sampling 195
7.2 The Binomial Distribution 198
7.3 The Hypergeometric Distribution 201
7.4 Posterior Distributions 202
7.5 Mean Squared Error in Estimation 206
7.6 Testing Hypotheses About p 208
Chapter O Rectangular Games 217
8.1 Minimax Strategies 219
8.2 Saddle Points 222
8.3 Mixed Strategies 226
8.4 Relation to the Decision Problem 228
8.5 Linear Programming 233
8.6 The Simplex Method 237
Chapter y Sequential Procedures 245
9.1 Basic Definitions 247
9.2 Bayesian Procedures 250
9.3 Hypothesis Testing—One More Observation? 256
9.4 The Bayes Sequential Test—Two Actions 263
9.5 The Classical Sequential Likelihood Ratio Test 267
xii Contents
References 275
Appendix—Tables 277
Table A l The Standard Normal Distribution Function 278
Table A 2 Binomial Probabilities 280
Table A 3 The Poisson Distribution 281
Answers to Problems 285
Index 291
|
| any_adam_object | 1 |
| author | Lindgren, Bernard W. 1924- |
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| dewey-full | 519.5/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/4 |
| dewey-search | 519.5/4 |
| dewey-sort | 3519.5 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV001938657 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:34Z |
| institution | BVB |
| language | English |
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| physical | XII, 292 S. Illustrationen |
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| publishDate | 1971 |
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| publisher | Macmillan [u.a.] |
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| spelling | Lindgren, Bernard W. 1924- Verfasser (DE-588)172227216 aut Elements of decision theory B. W. Lindgren New York Macmillan [u.a.] 1971 XII, 292 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Statistical decision Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001263558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lindgren, Bernard W. 1924- Elements of decision theory Statistical decision Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4138606-1 |
| title | Elements of decision theory |
| title_auth | Elements of decision theory |
| title_exact_search | Elements of decision theory |
| title_full | Elements of decision theory B. W. Lindgren |
| title_fullStr | Elements of decision theory B. W. Lindgren |
| title_full_unstemmed | Elements of decision theory B. W. Lindgren |
| title_short | Elements of decision theory |
| title_sort | elements of decision theory |
| topic | Statistical decision Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Statistical decision Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001263558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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