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
Postulates of a personalistic theory of decision | 1 |
Consequences acts and decisions | 10 |
The simple ordering of acts with respect to preference | 17 |
PERSONAL PROBABILITY | 28 |
OBSERVATION | 47 |
CRITICAL COMMENTS ON PERSONAL PROBABILITY | 58 |
UTILITY | 72 |
Small worlds | 83 |
Sequential probability ratio procedures | 215 |
Randomization | 216 |
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 |
Historical and critical comments on utility | 93 |
PARTITION PROBLEMS | 120 |
STATISTICS PROPER | 154 |
A PERSONALISTIC REINTERPRETATION OF THE MINIMAX THEORY | 172 |
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 |
A behavioralistic review concluded | 244 |
TESTING 1 Introduction | 246 |
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 B₂ basic acts behavior Bernoulli Bibliography bilinear games bility called chapter concept condition conditional probability consequences considered context convex convex set Criterion decision problem defined definition derived act discussion dominates elements equal equivalent example Exercise expected value f and g Finetti finite number formal function gambles grand-world 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 partition problems personal probability personalistic view possible postulate preference proba probability measure PROOF random variables real numbers seems sense sequence situation small world sufficient statistics suppose sure-thing principle symmetry technical testing Theorem theory of personal tion typically utility verbalistic Wald