## 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 |

PsasoNAL PnoBABILITY | 27 |

irs on PnnsoxaL Paosaamrrr | 53 |

UnLrrY | 71 |

10 | 109 |

PARTITIoN PnoaLsus | 116 |

13 | 132 |

17 | 139 |

Mixed acts in statistics | 217 |

Ponrr ESTIMATIoN 1 Introduction | 220 |

27 | 221 |

Criteria that have been proposed for point estimates | 223 |

A behavioralistic review of the criteria for point estimation I | 229 |

A behavioralistic review continued | 234 |

A behavioralistic review concluded | 244 |

Tnsrmo 1 Introduction | 246 |

Srarrsrrcs | 154 |

PaaaLLausu BETWEEN THE Mrsruax TaroRY AND ran TuaoRr | 178 |

Tan IAIHEhlAlICS or MiNruax PaoaLaus | 184 |

Bilinear games | 186 |

An example of a bilinear game | 189 |

Bilinear games exhibiting symmetry | 193 |

Mr m x Rows 1 Introduction | 200 |

Utility and the minimax rule | 201 |

Almost subminimax acts | 203 |

The minimax rule does not generate a simple ordering | 205 |

0 T0 OnsnnvxrroNs 1 Introduction | 208 |

Suﬁcient statistics | 212 |

The approach to certainty | 214 |

Sequential probability ratio procedues | 215 |

Randomization | 216 |

A theory of testing | 247 |

Testing in practice | 252 |

IrrrznvaL EsrlmanoN AND RELATED Torres 1 Estimates of the accuracy of estimates | 257 |

Interval estimation and conﬁdence intervals | 259 |

Tolerance intervals | 262 |

cnn VALUE | 263 |

Convex FUNcrIoNS | 266 |

aLu | 270 |

43 | 271 |

Bmuocaarnrc SoreLzmsrvr | 283 |

TzcnmcaL SYMBoLS | 299 |

Arrrnoa Irmax | 301 |

305 | |

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### Common terms and phrases

according acts actually agree analysis apply associated 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 ﬁrst formal function Gamble given hold idea illustrate implies important income independent inﬁnite interest interpretation interval introduction least less linear logic loss mathematical mean measure minimax minimax rule necessary objectivistic observation obtains particular partition person personal probability personalistic positive possible postulate practical preference present principle probability question random variables reader reason regarded relation respectively seems sense sequence simple situation statistics suggested Suppose Table technical testing Theorem theory tion typically utility