The Foundations of StatisticsClassic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended. |
Contents
PRELIMINARY CONSIDERATIONS ON DECISION IN THE FACE OF UNCERTAINTY | 6 |
PERSONAL PROBABILITY | 27 |
OBSERVATION | 47 |
CRITICAL COMMENTS ON PERSONAL PROBABILITY | 56 |
UTILITY | 69 |
PARTITION PROBLEMS | 120 |
STATISTICS PROPER | 154 |
A PERSONALISTIC REINTERPRETATION OF THE MINIMAX THEORY | 172 |
Mixed acts in statistics | 217 |
POINT ESTIMATION 1 Introduction | 220 |
The verbalistic concept of point estimation | 221 |
Criteria that have been proposed for point estimates | 223 |
A behavioralistic review of the criteria for point estimation | 229 |
A behavioralistic review continued | 234 |
A behavioralistic review concluded | 244 |
TESTING 1 Introduction | 246 |
THE PARALLELISM BETWEEN THE MINIMAX THEORY AND THE THEORY | 178 |
THE MATHEMATICS OF MINIMAX PROBLEMS | 184 |
Bilinear games | 186 |
An example of a bilinear game | 189 |
Bilinear games exhibiting symmetry | 193 |
OBJECTIONS TO THE MINIMAX RULES 1 Introduction | 200 |
Utility and the minimax rule | 201 |
Almost subminimax acts | 203 |
The minimax rule does not generate a simple ordering | 205 |
THE MINIMAX THEORY APPLIED TO OBSERVATIONS 1 Introduction | 208 |
Sufficient statistics | 212 |
The approach to certainty | 214 |
Sequential probability ratio procedures | 215 |
Randomization | 216 |
A theory of testing | 247 |
Testing in practice | 252 |
INTERVAL ESTIMATION AND RELATED TOPICS 1 Estimates of the accuracy of estimates | 257 |
Interval estimation and confidence intervals | 259 |
Tolerance intervals | 262 |
EXPECTED VALUE | 263 |
CONVEX FUNCTIONS | 266 |
BIBLIOGRAPHIC MATERIAL | 270 |
BIBLIOGRAPHIC SUPPLEMENT | 283 |
TECHNICAL SYMBOLS | 299 |
AUTHOR INDEX | 301 |
| 305 | |
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Common terms and phrases
act f analysis Annals of Mathematical applications B₁ basic acts behavior bibliography bilinear games bility called chapter concept conditional conditional probability consequences consider context convex Criterion decision problem defined definition derived act discussion distribution dominates elements equal equivalent example Exercise expected value f and g Finetti finite number formal function Gamble given hypothesis idea implies infinite interpretation interval estimation L. J. Savage least likelihood ratio likelihood-ratio test linear logic loss loss function lottery Mathematical Statistics max L(f maximin minimax rule minimax theory mixed acts n-tuples notion null objectivistic objectivistic views observation particular partition problems personal probability personalistic view possible postulate preference proba probability measure random variables real numbers seems sequence situation small world sufficient statistics Suppose sure-thing principle symmetry technical testing Theorem theory of personal theory of probability tion typically utility verbalistic Wald