## 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

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

act f analysis apply basic acts behavior behavioralistic Bernoulli bilinear games called chapter concept condition conditional probability conﬁned consequences considered context convex convex set Criterion decision problem deﬁned deﬁnition derived act discussion dominates elements equal equivalent example Exercise expected value f 5 g f and g ﬁnd Finetti ﬁnite number ﬁnite set ﬁrst ﬁve ﬁxed formal g given Gamble hypothesis idea implies income inﬁnite interpretation interval estimation justiﬁed least likelihood ratio likelihood-ratio test linear logic loss function lottery max L(f maximin 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 postulate preference probability measure qualitative probability random variables real numbers satisﬁes seems sequence situation small world sufﬁcient sufficient statistics suﬁicient Suppose sure-thing principle symmetry testing Theorem tion typically utility verbalistic veriﬁed Wald