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Understanding Uncertainty |
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Contents |
7 |
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Preface |
13 |
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Prologue |
15 |
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Chapter 1: Uncertainty |
19 |
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1.1. Introduction |
19 |
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1.2. Examples |
20 |
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1.3. Suppression of Uncertainty |
29 |
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1.4. The Removal of Uncertainty |
31 |
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1.5. The Uses of Uncertainty |
33 |
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1.6. The Calculus of Uncertainty |
35 |
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1.7. Beliefs |
36 |
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1.8. Decision Analysis |
38 |
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Chapter 2: Stylistic Questions |
41 |
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2.1. Reason |
41 |
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2.2. Unreason |
44 |
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2.3. Facts |
46 |
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2.4. Emotion |
47 |
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2.5. Normative and Descriptive Approaches |
49 |
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2.6. Simplicity |
51 |
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2.7. Mathematics |
53 |
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2.8. Writing |
55 |
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2.9. Mathematics Tutorial |
56 |
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Chapter 3: Probability |
63 |
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3.1. Measurement |
63 |
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3.2. Randomness |
66 |
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3.3. A Standard for Probability |
68 |
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3.4. Probability |
70 |
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3.5. Coherence |
72 |
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3.6. Belief |
74 |
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3.7. Complementary Event |
76 |
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3.8. Odds |
78 |
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3.9. Knowledge Base |
81 |
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3.10. Examples |
84 |
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3.11. Retrospect |
86 |
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Chapter 4: Two Events |
87 |
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4.1. Two Events |
87 |
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4.2. Conditional Probability |
90 |
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4.3. Independence |
93 |
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4.4. Association |
95 |
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4.5. Examples |
97 |
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4.6. Supposition and Fact |
99 |
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4.7. Seeing and Doing |
100 |
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Chapter 5: The Rules of Probability |
103 |
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5.1. Combinations of Events |
103 |
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5.2. Addition Rule |
105 |
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5.3. Multiplication Rule |
107 |
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5.4. The Basic Rules |
110 |
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5.5. Examples |
113 |
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5.6. Extension of the Conversation |
116 |
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5.7. Dutch Books |
119 |
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5.8. Scoring Rules |
121 |
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5.9. Logic Again |
123 |
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5.10. Decision Analysis |
124 |
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5.11. The Prisoners’ Dilemma |
125 |
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5.12. The Calculus and Reality |
128 |
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5.13. Closure |
130 |
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Chapter 6: Bayes Rule |
131 |
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6.1. Transposed Conditionals |
131 |
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6.2. Learning |
134 |
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6.3. Bayes Rule |
136 |
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6.4. Medical Diagnosis |
137 |
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6.5. Odds Form of Bayes Rule |
141 |
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6.6. Forensic Evidence |
143 |
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6.7. Likelihood Ratio |
145 |
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6.8. Cromwell’s Rule |
147 |
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6.9. A Tale of Two Urns |
149 |
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6.10. Ravens |
153 |
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6.11. Diagnosis and Related Matters |
156 |
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6.12. Information |
158 |
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Chapter 7: Measuring Uncertainty |
161 |
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7.1. Classical Form |
161 |
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7.2. Frequency Data |
163 |
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7.3. Exchangeability |
165 |
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7.4. Bernoulli Series |
169 |
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7.5. De Finetti’s Result |
170 |
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7.6. Large Numbers |
172 |
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7.7. Belief and Frequency |
175 |
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7.8. Chance |
179 |
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Chapter 8: Three Events |
183 |
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8.1. The Rules of Probability |
183 |
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8.2. Simpson’s Paradox |
186 |
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8.3. Source of the Paradox |
188 |
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8.4. Experimentation |
189 |
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8.5. Randomization |
191 |
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8.6. Exchangeability |
194 |
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8.7. Spurious Association |
199 |
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8.8. Independence |
201 |
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8.9. Conclusions |
204 |
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Chapter 9: Variation |
207 |
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9.1. Variation and Uncertainty |
207 |
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9.2. Binomial Distribution |
209 |
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9.3. Expectation |
213 |
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9.4. Poisson Distribution |
215 |
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9.5. Spread |
219 |
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9.6. Variability as an Experimental Tool |
222 |
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9.7. Probability and Chance |
224 |
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9.8. Pictorial Representation |
226 |
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9.9. Probability Densities |
230 |
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9.10. The Normal Distribution |
231 |
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9.11. Variation as a Natural Phenomenon |
235 |
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9.12. Ellsberg’s Paradox |
237 |
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Chapter 10: Decision Analysis |
243 |
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10.1. Beliefs and Actions |
243 |
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10.2. Comparison of Consequences |
245 |
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10.3. Medical Example |
249 |
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10.4. Maximization of Expected Utility |
252 |
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10.5. More on Utility |
254 |
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10.6. Some Complications |
256 |
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10.7. Reason and Emotion |
258 |
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10.8. Numeracy |
260 |
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10.9. Expected Utility |
263 |
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10.10. Decision Trees |
264 |
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10.11. The Art and Science of Decision Analysis |
267 |
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10.12. Further Complications |
270 |
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10.13. Combination of Features |
274 |
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10.14. Legal Applications |
278 |
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Chapter 11: Science |
283 |
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11.1. Scientific Method |
283 |
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11.2. Science and Education |
284 |
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11.3. Data Uncertainty |
286 |
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11.4. Theories |
289 |
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11.5. Uncertainty of a Theory |
294 |
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11.6. The Bayesian Development |
296 |
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11.7. Modification of Theories |
299 |
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11.8. Models |
302 |
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11.9. Hypothesis Testing |
305 |
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11.10. Significance Tests |
309 |
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11.11. Repetition |
311 |
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11.12. Summary |
314 |
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Chapter 12: Examples |
317 |
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12.1. Introduction |
317 |
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12.2. Cards |
318 |
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12.3. The Three Doors |
319 |
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12.4. The Problem of Two Daughters |
323 |
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12.5. Two More Daughters and Cardano |
327 |
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12.6. The Two Envelopes |
331 |
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12.7. Y2K |
334 |
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12.8. UFOs |
335 |
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12.9. Conglomerability |
339 |
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12.10. Efron’s Dice |
341 |
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Chapter 13: Probability Assessment |
345 |
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13.1. Nonrepeatable Events |
345 |
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13.2. Two Events |
347 |
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13.3. Coherence |
351 |
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13.4. Probabilistic Reasoning |
354 |
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13.5. Trickle Down |
355 |
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13.6. Summary |
359 |
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Chapter 14: Statistics |
361 |
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14.1. Bayesian Statistics |
361 |
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14.2. A Bayesian Example |
364 |
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14.3. Frequency Statistics |
368 |
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14.4. Significance Tests |
373 |
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14.5. Betting |
378 |
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14.6. Finance |
383 |
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Epilogue |
393 |
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Subject Index |
401 |
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Index of Examples |
409 |
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Index of Notations |
411 |
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