## 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. |

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### Contents

Postulates of a personalistic theory of decision End papers | 1 |

The person | 7 |

Consequences acts and decisions | 13 |

The surething principle | 21 |

PERSONAL PROBABILITY | 28 |

OBSERVATION | 47 |

CRITICAL CoMMENTs on PERSONAL PROBABILITY | 58 |

UTILITY | 72 |

Mixed acts in statistics | 217 |

PoſNT 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 |

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 |

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 WALUE | 263 |

CoNVEx FUNCTIONs | 266 |

BIBLIoGRAPHIC MATERIAL | 270 |

56 | 275 |

BIBLIOGRAPHIC SUPPLEMENT | 283 |

295 | |

TECHNICAL SYMBOLS | 299 |

AUTHOR INDEX | 301 |

302 | |

305 | |

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### Common terms and phrases

act f analysis Annals of Mathematical applications basic acts behavior behavioralistic Bernoulli bilinear games called chapter concept condition conditional probability confined consequences considered context convex convex set Corollary Criterion decision problem defined definition derived act discussion distribution dominates elements equal equivalent example Exercise expected value extension f and g Finetti finite number formal g given Gamble grand-world hypothesis idea implies income inequality infinite interpretation interval estimation least likelihood ratio likelihood-ratio test linear logic loss function lottery Mathematical Statistics max L(f maximin maximum-likelihood estimates minimax rule minimax theory mixed acts n-tuples notion null objectivistic objectivistic decision problem objectivistic views observation particular partition problems personal probability personalistic view possible postulates preference prob probability measure random variable real numbers seems sense sequence sequential situation small world sufficient statistics Suppose sure-thing principle symmetry testing Theorem tion typically utility verbalistic Wald