Subjective Probability: The Real Thing

Half-title......Page 2
Title......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
Acknowledgments......Page 13
Odds m:n correspond to probability…......Page 18
Questions......Page 19
Discussion......Page 20
1.2 Why Probabilities Are Additive......Page 21
1.2.1 Dutch Book Argument for Finite Additivity......Page 22
1.2.2 Dutch Book Argument for Countable Additivity......Page 25
De Morgan\'s Laws......Page 26
1.4 Conditional Probability......Page 29
1.5 Why \"|\" Cannot Be a Connective......Page 32
1.6 Bayes\'s Theorem......Page 33
Definitions......Page 34
1.8 Objective Chance......Page 36
1.9 Supplements......Page 39
2 Testing Scientific Theories......Page 46
2.1 Quantifications of Confirmation......Page 47
2.2 Observation and Sufficiency......Page 49
2.3 Leverrier on Neptune......Page 51
2.4 Dorling on the Duhem Problem......Page 52
2.4.1 Einstein/Newton, 1919......Page 54
2.4.2 Bell\'s Inequalities: Holt/Clauser......Page 55
2.4.3 Laplace/Adams......Page 58
2.4.4 Dorling\'s Conclusions......Page 59
2.5 Old News Explained......Page 61
2.6 Supplements......Page 65
3.1 Conditioning......Page 68
3.2 Generalized Conditioning......Page 70
3.3 Probabilistic Observation Reports......Page 72
3.4 Updating Twice: Commutativity......Page 74
3.4.2 Updating on Alien Factors for Diagnoses......Page 75
3.5 Softcore Empiricism......Page 76
4.1 Probability and Expectation......Page 79
4.2 Conditional Expectation......Page 80
4.3 Laws of Expectation......Page 82
4.4 Median and Mean......Page 84
4.5 Variance......Page 87
4.6 A Law of Large Numbers......Page 89
4.7.3 Many Pairwise Uncorrelated R.V.\'s......Page 90
4.7.4 Corollary: Bernoulli Trials......Page 91
4.7.5 Noncorrelation and Independence......Page 92
5.1.1 Probabilities from Statistics: Minimalism......Page 93
5.1.2 Probabilities from Statistics: Exchangeability......Page 95
5.1.3 Exchangeability: Urn Examples......Page 96
5.1.4 Supplements......Page 98
Diaconis and Freedman on de Finetti\'s Generalizations of Exchangeability......Page 99
5.2 Exchangeability Itself......Page 100
5.3 Two Species of Partial Exchangeability......Page 102
5.3.2 Markov Dependency......Page 103
5.4 Finite Forms of de Finetti’s Theorem on Partial Exchangeability......Page 105
5.5 Technical Interpolation: Infinite Forms......Page 107
5.6 Concluding Remarks......Page 110
Technical Interpolations (2–4)......Page 112
6.1 Preference Logic......Page 115
6.1.1 Denial Reverses Preferences…......Page 116
6.1.3 The “Sure Thing” (or “Dominance”) Principle…......Page 117
6.1.3.1 BJ-ing the MM......Page 118
6.1.4 Bayesian Frames......Page 119
6.2 Causality......Page 120
6.3 Supplements: Newcomb Problems......Page 122
6.3.1 \"The Mild and Soothing Weed\"......Page 123
6.3.2 The Flagship Newcomb Problem......Page 126
6.3.3 Hofstadter......Page 128
6.3.4 Conclusion......Page 129
References......Page 132
Index......Page 138