A discussion of how the failure of the financial sector to use the proper approach
Table of Contents
Preface xi
Prologue xiii
1. Uncertainty 1
1.1. 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 11
1.7. Beliefs 12
1.8. Decision Analysis 13
2. Stylistic Questions 15
2.1. Reason 15
2.2. Unreason 17
Literature 17
Advertising 17
Politics 18
Law 18
Television 18
2.3. Facts 19
2.4. Emotion 19
2.5. Prescriptive and Descriptive Approaches 20
2.6. Simplicity 22
2.7. Mathematics 23
2.8. Writing 25
2.9. Mathematics Tutorial 26
3. Probability 30
3.1. Measurement 30
3.2. Randomness 32
3.3. A Standard for Probability 34
3.4. Probability 35
3.5. Coherence 36
3.6. Belief 37
3.7. Complementary Event 39
3.8. Odds 40
3.9. Knowledge Base 43
3.10. Examples 44
3.11. Retrospect 46
4. Two Events 47
4.1. Two Events 47
4.2. Conditional Probability 49
4.3. Independence 51
4.4. Association 53
4.5. Examples 54
4.6. Supposition and Fact 56
4.7. Seeing and Doing 57
5. The Rules of Probability 59
5.1. Combinations of Events 59
5.2. Addition Rule 61
5.3. Multiplication Rule 62
5.4. The Basic Rules 64
5.5. Examples 66
5.6. Extension of the Conversation 68
5.7. Dutch Books 70
5.8. Scoring Rules 72
5.9. Logic Again 73
5.10. Decision Analysis 74
5.11. The Prisoners’ Dilemma 75
5.12. The Calculus and Reality 76
6. Bayes Rule 79
6.1. Transposed Conditionals 79
6.2. Learning 81
6.3. Bayes Rule 82
6.4. Medical Diagnosis 83
6.5. Odds Form of Bayes Rule 86
6.6. Forensic Evidence 88
6.7. Likelihood Ratio 89
6.8. Cromwell’s Rule 90
6.9. A Tale of Two Urns 92
6.10. 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
7.5. De Finetti’s Result 107
7.6. Large Numbers 109
7.7. Belief and Frequency 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. Experimentation 122
8.5. Randomization 123
8.6. Exchangeability 125
8.7. Spurious Association 128
8.8. Independence 130
8.9. Conclusions 132
9. Variation 134
9.1. Variation 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. Probability 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
10. Decision Analysis 158 10.1. Beliefs and Actions 158
10.2. Comparison of Consequences 160
10.3. Medical Example 162
10.4. Maximization of Expected Utility 164
10.5. More on Utility 165
10.6. Some Complications 167
10.7. Reason and Emotion 168
10.8. Numeracy 170
10.9. Expected Utility 171
10.10. Decision Trees 172
10.11. The Art and Science of Decision Analysis 175
10.12. Further Complications 177
10.13. Combination of Features 179
10.14. Legal Applications 182
11. Science 186
11.1. Scientific Method 186
11.2. Science and Education 187
11.3. Data Uncertainty 188
11.4. Theories 190
11.5. Uncertainty of a Theory 193
11.6. The Bayesian Development 195
11.7. Modification of Theories 197
11.8. Models 199
11.9. Hypothesis Testing 202
11.10. Significance Tests 204
11.11. Repetition 206
11.12. Summary 208
12. Examples 211
12.1. Introduction 211
12.2. Cards 212
12.3. The Three Doors 213
12.4. The Newcomers to Your Street 215
12.5. The Two Envelopes 217
12.6. Y2K 220
12.7. UFOs 221
12.8. Conglomerability 224
13. Probability Assessment 226
13.1. Nonrepeatable Events 226
13.2. Two Events 227
13.3. Coherence 230
13.4. Probabilistic Reasoning 233
13.5. Trickle Down 234
13.6. Summary 236
Epilogue 238
Subject Index 243
Index of Examples 248
Index of Notations 250
