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1, Uncertainty 1 SIo. Introduction 1 1.2. Examples 2 1.3. Suppression of Uncertainty 7 1 4. The Removal of Uncertainty 8 1.5. The Uses of Uncertainty 9 1.6. The Calculus of Uncertainty 1 1.7. Beliefs 12 1.8. Decision Analysis 13 2. Stylistic Questions 15 .1. Reason 15 2.2. Unreason 17 Literature 17 Advertising 17 Politics 18 Law 18 Television 18 23. Facts 19 2.4. Emotion 19 2.5. Prescriptive and Descriptive Approaches 20 '2 Simnlplicitv 2.7'. athematics 9. Lahcmatics Tutorial 26 "3. Prolability 30 -. N. easuremient 30 .,2. Randomness 32 3.3, A Standard for P-rbability 3.4. Probability -5 3.5. Coherence 35 3.6- Belief 3.. ( omiplementary Event 39 3.8. Odds 40 "3.9. Knowledge Base 3. I0. LExamples 44 311. Retrospect 46 . o Events 47 4 1. Two Events 47 4.2. Conditional Probability 49 4.3. Independen ce 51 4.4, Association i. 4.5,. xa imples p 4,0. Supposition and Fact 56 .7. Seeing and Doing 57 5. The Rules of Probability 59 5.1. Combhi ations of Evc:ts 5.. 1 Ldd ion Rule 6 5.3. NMtulpipcation Rule 62 5.4. The Basic Rules 64 5.5. Examples 66 5.6. Extensioln of the Conversation 68 "5/7, Dutch Books 0 5.8. Scoring Rules O, Decision Analvsis 74 S1 Tine fPrisoners' Dilemma T .2 T.h C aculus and Reality. .- 6, Bayes Rule 79 6. i.Trans,posed (C,oiii onr i < L- t . . .. a f^.^. -.L- birnii0'"i- . 6.3. hayes Rule 82 6.4. Medical Diagnosis 83 65. Odds Form of Bayes Rule 86 6.6 Forensic Evidence 88 6.7. Likelihood Ratio 89 6.8. Cronwells Rule 90 6.9. A Tale of Two Urns 92 61 0. Ravens 94 6.11 Diagnosis and Related Matters 97 6.12. Information 98 7. Measuring Uncertainty 101 7.1. Classical Form 101 7.2. Frequency Data 103 "7.3 Exchangeability 104 7.4. Bernoulli Series 106 75. De Finetti s Result 107 7.6. Large Numbers 109 77. Belief and Frequiency . 111 7 8. Chance 114 8. Three Events 117 8.1. The Rules of Probability 117 8.2. Simpson's Paradox 119 8.3. Source of the Paradox 121 8.4. Experinmentation 122 8.5. Randomization 123 8.6. Exchangeability 125 8.7 Spurious Association 128 8.. Independence 130 8.9. Conclusions 132 9. Variation 134 9.. 1 Vriation and Uncertainty 134 9.2. Binomial Distribution 135 9.3. Expectation 137 9.4. Poisson Distribution 139 9.5. Spread 142 9.6. Variability as an Experimental Tool 144 9.7 Probabiliy and Chance 145 9.8 Pictorial Representation 147 9,9. The Normal Distribution 150 "9.10. Variation as a Natural Phenomenon 152 9. 11. Ellsberg's Paradox 154 0O. Deisi:on Analysis 158 0.1. Beliefs and Actions 158 10,2. Comparison of Consequences 160 103. Medical Example 162 10.4. Maximization of Exp cted Utility 64 10.5. More on Utility 165 10.6. Some Complications 167 10.7. Reason and Emotion 168 S10,. Numeracy 170 10.9. Expected Utili t 171 10 10. Decision Trees 172 10. I. The Art and Science of Decision Analysis 175 10.1 2. Further Complications 177 10. 3. Combination of Features 179 10.14. Leal Applications 18i 11. Science 186 1.. 1. Scientific Method 186 Si .2. Science and Education 87 1 i3, Data Uncertainty 188 I 1.4. T heores 190 1 1.5. incert inty of a Theory 193 i 16. The Bayesian Development 195 1 1. 7 Modification of Theories 197 SL8.. Models 199 1 I.. Hypothesis Testing 202 1 1 i0. Significance Tests 204 I_ I . Repetition 206 1 1 12. Summary 208 12. Exaiples 211 12 1 . Introduction 211 :2.2. Cards 212 S2.3. The Three Doors 213 S 2.4. The Newcolmers to our Street 215 12. The Two Envelopes 217 12.6A Y K 220 1 2,/7, L s 221 12.' C onlomnerabilit, 224 13 Probabilitfr Assessment 226 13.1. Nonrepeatabe Events 226 13.2. Two Events 227 13,3. Coherence 230 13.. Probabilistic Reasoning 233 13.5 Trickle Down 234 13.6. Summary 236