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