## 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 | 1 |

PERSONAL PROBABILITY | 28 |

OBSERVATION | 47 |

CRITICAL COMMENTS ON PERSONAL PROBABILITY | 58 |

UTILITY | 72 |

Small worlds | 83 |

Historical and critical comments on utility | 93 |

10 | 100 |

Randomization | 216 |

Mixed acts in statistics | 217 |

POINT ESTIMATION 1 Introduction | 220 |

27 | 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 |

30 | 241 |

PARTITION PROBLEMS | 120 |

13 | 132 |

17 | 139 |

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 |

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 |

40 | 280 |

BIBLIOGRAPHIC SUPPLEMENT | 283 |

TECHNICAL SYMBOLS | 299 |

AUTHOR INDEX | 301 |

305 | |

306 | |

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### Common terms and phrases

according acts actually agree analysis applications associated B₁ basic called chapter concept condition confined connection consequences consideration considered context convex corresponding course Criterion decide decision problem defined definition derived discussion distribution dominates elements equal equivalent estimate example Exercise exists expected experience expressed extension fact finite formal function Gamble given idea illustrate implies important income independent interest interpretation interval introduction Journal least less linear logic loss mathematical mean measure minimax minimax rule necessary objectivistic observation obtains particular partition person personal probability personalistic positive possible postulates practical present Press principle probability random variable reader reason reference regarded respectively seems sense sequence situations statistics sufficient suggested Suppose Table technical testing Theorem theory tion typically University utility York