Subjective Probability: The Real Thing

✍ Scribed by Richard Jeffrey

• Publisher: Cambridge University Press
• Year: 2004
• Tongue: English
• Leaves: 142
• Category: Library

✦ Synopsis

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability theory is a mode of judgement. Written by one of the greatest figures in the field of probability theory, the book is both a summation and a synthesis of a lifetime of wrestling with such problems and issues.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Acknowledgments......Page 14
Odds m:n correspond to probability…......Page 19
Questions......Page 20
Discussion......Page 21
1.2 Why Probabilities Are Additive......Page 22
1.2.1 Dutch Book Argument for Finite Additivity......Page 23
1.2.2 Dutch Book Argument for Countable Additivity......Page 26
De Morgan’s Laws......Page 27
1.4 Conditional Probability......Page 30
1.5 Why “|” Cannot Be a Connective......Page 33
1.6 Bayes’s Theorem......Page 34
Definitions......Page 35
1.8 Objective Chance......Page 37
1.9 Supplements......Page 40
2 Testing Scientific Theories......Page 47
2.1 Quantifications of Confirmation......Page 48
2.2 Observation and Sufficiency......Page 50
2.3 Leverrier on Neptune......Page 52
2.4 Dorling on the Duhem Problem......Page 53
2.4.1 Einstein/Newton, 1919......Page 55
2.4.2 Bell’s Inequalities: Holt/Clauser......Page 56
2.4.3 Laplace/Adams......Page 59
2.4.4 Dorling’s Conclusions......Page 60
2.5 Old News Explained......Page 62
2.6 Supplements......Page 66
3.1 Conditioning......Page 69
3.2 Generalized Conditioning......Page 71
3.3 Probabilistic Observation Reports......Page 73
3.4 Updating Twice: Commutativity......Page 75
3.4.2 Updating on Alien Factors for Diagnoses......Page 76
3.5 Softcore Empiricism......Page 77
4.1 Probability and Expectation......Page 80
4.2 Conditional Expectation......Page 81
4.3 Laws of Expectation......Page 83
4.4 Median and Mean......Page 85
4.5 Variance......Page 88
4.6 A Law of Large Numbers......Page 90
4.7.3 Many Pairwise Uncorrelated R.V.’s......Page 91
4.7.4 Corollary: Bernoulli Trials......Page 92
4.7.5 Noncorrelation and Independence......Page 93
5.1.1 Probabilities from Statistics: Minimalism......Page 94
5.1.2 Probabilities from Statistics: Exchangeability......Page 96
5.1.3 Exchangeability: Urn Examples......Page 97
5.1.4 Supplements......Page 99
Diaconis and Freedman on de Finetti’s Generalizations of Exchangeability......Page 100
5.2 Exchangeability Itself......Page 101
5.3 Two Species of Partial Exchangeability......Page 103
5.3.2 Markov Dependency......Page 104
5.4 Finite Forms of de Finetti’s Theorem on Partial Exchangeability......Page 106
5.5 Technical Interpolation: Infinite Forms......Page 108
5.6 Concluding Remarks......Page 111
Technical Interpolations (2–4)......Page 113
6.1 Preference Logic......Page 116
6.1.1 Denial Reverses Preferences…......Page 117
6.1.3 The “Sure Thing” (or “Dominance”) Principle…......Page 118
6.1.3.1 BJ-ing the MM......Page 119
6.1.4 Bayesian Frames......Page 120
6.2 Causality......Page 121
6.3 Supplements: Newcomb Problems......Page 123
6.3.1 “The Mild and Soothing Weed”......Page 124
6.3.2 The Flagship Newcomb Problem......Page 127
6.3.3 Hofstadter......Page 129
6.3.4 Conclusion......Page 130
References......Page 133
Index......Page 139