Understanding Uncertainty, Revised Edition

<p>Preface xi</p>
<p>Prologue xiii</p>
<p>1. Uncertainty 1</p>
<p>1.1. Introduction 1</p>
<p>1.2. Examples 2</p>
<p>1.3. Suppression of Uncertainty 7</p>
<p>1.4. The Removal of Uncertainty 8</p>
<p>1.5. The Uses of Uncertainty 9</p>
<p>1.6. The Calculus of Uncertainty 11</p>
<p>1.7. Beliefs 12</p>
<p>1.8. Decision Analysis 13</p>
<p>2. Stylistic Questions 15</p>
<p>2.1. Reason 15</p>
<p>2.2. Unreason 17</p>
<p>Literature 17</p>
<p>Advertising 17</p>
<p>Politics 18</p>
<p>Law 18</p>
<p>Television 18</p>
<p>2.3. Facts 19</p>
<p>2.4. Emotion 19</p>
<p>2.5. Prescriptive and Descriptive Approaches 20</p>
<p>2.6. Simplicity 22</p>
<p>2.7. Mathematics 23</p>
<p>2.8. Writing 25</p>
<p>2.9. Mathematics Tutorial 26</p>
<p>3. Probability 30</p>
<p>3.1. Measurement 30</p>
<p>3.2. Randomness 32</p>
<p>3.3. A Standard for Probability 34</p>
<p>3.4. Probability 35</p>
<p>3.5. Coherence 36</p>
<p>3.6. Belief 37</p>
<p>3.7. Complementary Event 39</p>
<p>3.8. Odds 40</p>
<p>3.9. Knowledge Base 43</p>
<p>3.10. Examples 44</p>
<p>3.11. Retrospect 46</p>
<p>4. Two Events 47</p>
<p>4.1. Two Events 47</p>
<p>4.2. Conditional Probability 49</p>
<p>4.3. Independence 51</p>
<p>4.4. Association 53</p>
<p>4.5. Examples 54</p>
<p>4.6. Supposition and Fact 56</p>
<p>4.7. Seeing and Doing 57</p>
<p>5. The Rules of Probability 59</p>
<p>5.1. Combinations of Events 59</p>
<p>5.2. Addition Rule 61</p>
<p>5.3. Multiplication Rule 62</p>
<p>5.4. The Basic Rules 64</p>
<p>5.5. Examples 66</p>
<p>5.6. Extension of the Conversation 68</p>
<p>5.7. Dutch Books 70</p>
<p>5.8. Scoring Rules 72</p>
<p>5.9. Logic Again 73</p>
<p>5.10. Decision Analysis 74</p>
<p>5.11. The Prisoners Dilemma 75</p>
<p>5.12. The Calculus and Reality 76</p>
<p>6. Bayes Rule 79</p>
<p>6.1. Transposed Conditionals 79</p>
<p>6.2. Learning 81</p>
<p>6.3. Bayes Rule 82</p>
<p>6.4. Medical Diagnosis 83</p>
<p>6.5. Odds Form of Bayes Rule 86</p>
<p>6.6. Forensic Evidence 88</p>
<p>6.7. Likelihood Ratio 89</p>
<p>6.8. Cromwell s Rule 90</p>
<p>6.9. A Tale of Two Urns 92</p>
<p>6.10. Ravens 94</p>
<p>6.11. Diagnosis and Related Matters 97</p>
<p>6.12. Information 98</p>
<p>7. Measuring Uncertainty 101</p>
<p>7.1. Classical Form 101</p>
<p>7.2. Frequency Data 103</p>
<p>7.3. Exchangeability 104</p>
<p>7.4. Bernoulli Series 106</p>
<p>7.5. De Finetti s Result 107</p>
<p>7.6. Large Numbers 109</p>
<p>7.7. Belief and Frequency 111</p>
<p>7.8. Chance 114</p>
<p>8. Three Events 117</p>
<p>8.1. The Rules of Probability 117</p>
<p>8.2. Simpson s Paradox 119</p>
<p>8.3. Source of the Paradox 121</p>
<p>8.4. Experimentation 122</p>
<p>8.5. Randomization 123</p>
<p>8.6. Exchangeability 125</p>
<p>8.7. Spurious Association 128</p>
<p>8.8. Independence 130</p>
<p>8.9. Conclusions 132</p>
<p>9. Variation 134</p>
<p>9.1. Variation and Uncertainty 134</p>
<p>9.2. Binomial Distribution 135</p>
<p>9.3. Expectation 137</p>
<p>9.4. Poisson Distribution 139</p>
<p>9.5. Spread 142</p>
<p>9.6. Variability as an Experimental Tool 144</p>
<p>9.7. Probability and Chance 145</p>
<p>9.8. Pictorial Representation 147</p>
<p>9.9. The Normal Distribution 150</p>
<p>9.10. Variation as a Natural Phenomenon 152</p>
<p>9.11. Ellsberg s Paradox 154</p>
10. Decision Analysis 158
<p>10.1. Beliefs and Actions 158</p>
<p>10.2. Comparison of Consequences 160</p>
<p>10.3. Medical Example 162</p>
<p>10.4. Maximization of Expected Utility 164</p>
<p>10.5. More on Utility 165</p>
<p>10.6. Some Complications 167</p>
<p>10.7. Reason and Emotion 168</p>
<p>10.8. Numeracy 170</p>
<p>10.9. Expected Utility 171</p>
<p>10.10. Decision Trees 172</p>
<p>10.11. The Art and Science of Decision Analysis 175</p>
<p>10.12. Further Complications 177</p>
<p>10.13. Combination of Features 179</p>
<p>10.14. Legal Applications 182</p>
<p>11. Science 186</p>
<p>11.1. Scientific Method 186</p>
<p>11.2. Science and Education 187</p>
<p>11.3. Data Uncertainty 188</p>
<p>11.4. Theories 190</p>
<p>11.5. Uncertainty of a Theory 193</p>
<p>11.6. The Bayesian Development 195</p>
<p>11.7. Modification of Theories 197</p>
<p>11.8. Models 199</p>
<p>11.9. Hypothesis Testing 202</p>
<p>11.10. Significance Tests 204</p>
<p>11.11. Repetition 206</p>
<p>11.12. Summary 208</p>
<p>12. Examples 211</p>
<p>12.1. Introduction 211</p>
<p>12.2. Cards 212</p>
<p>12.3. The Three Doors 213</p>
<p>12.4. The Newcomers to Your Street 215</p>
<p>12.5. The Two Envelopes 217</p>
<p>12.6. Y2K 220</p>
<p>12.7. UFOs 221</p>
<p>12.8. Conglomerability 224</p>
<p>13. Probability Assessment 226</p>
<p>13.1. Nonrepeatable Events 226</p>
<p>13.2. Two Events 227</p>
<p>13.3. Coherence 230</p>
<p>13.4. Probabilistic Reasoning 233</p>
<p>13.5. Trickle Down 234</p>
<p>13.6. Summary 236</p>
<p>Epilogue 238</p>
<p>Subject Index 243</p>
<p>Index of Examples 248</p>
<p>Index of Notations 250</p>