Understanding Uncertainty

DENNIS V. LINDLEY is Professor Emeritus of Statistics and the former Head of Department at University College London. He is a Guy Medalist in Gold of the Royal Statistical Society and a founding organizer and former president of the celebrated Valencia International Meetings on Bayesian Statistics. Professor Lindley has published over 100 scholarly articles and several books, including Making Decisions, also published by Wiley.

• Preface xiPrologue xiii1. Uncertainty 11.1. Introduction 11.2. Examples 21.3. Suppression of Uncertainty 71.4. The Removal of Uncertainty 81.5. The Uses of Uncertainty 91.6. The Calculus of Uncertainty 111.7. Beliefs 121.8. Decision Analysis 132. Stylistic Questions 152.1. Reason 152.2. Unreason 17Literature 17Advertising 17Politics 18Law 18Television 182.3. Facts 192.4. Emotion 192.5. Prescriptive and Descriptive Approaches 202.6. Simplicity 222.7. Mathematics 232.8. Writing 252.9. Mathematics Tutorial 263. Probability 303.1. Measurement 303.2. Randomness 323.3. A Standard for Probability 343.4. Probability 353.5. Coherence 363.6. Belief 373.7. Complementary Event 393.8. Odds 403.9. Knowledge Base 433.10. Examples 443.11. Retrospect 464. Two Events 474.1. Two Events 474.2. Conditional Probability 494.3. Independence 514.4. Association 534.5. Examples 544.6. Supposition and Fact 564.7. Seeing and Doing 575. The Rules of Probability 595.1. Combinations of Events 595.2. Addition Rule 615.3. Multiplication Rule 625.4. The Basic Rules 645.5. Examples 665.6. Extension of the Conversation 685.7. Dutch Books 705.8. Scoring Rules 725.9. Logic Again 735.10. Decision Analysis 745.11. The Prisoners’ Dilemma 755.12. The Calculus and Reality 766. Bayes Rule 796.1. Transposed Conditionals 796.2. Learning 816.3. Bayes Rule 826.4. Medical Diagnosis 836.5. Odds Form of Bayes Rule 866.6. Forensic Evidence 886.7. Likelihood Ratio 896.8. Cromwell’s Rule 906.9. A Tale of Two Urns 926.10. Ravens 946.11. Diagnosis and Related Matters 976.12. Information 987. Measuring Uncertainty 1017.1. Classical Form 1017.2. Frequency Data 1037.3. Exchangeability 1047.4. Bernoulli Series 1067.5. De Finetti’s Result 1077.6. Large Numbers 1097.7. Belief and Frequency 1117.8. Chance 1148. Three Events 1178.1. The Rules of Probability 1178.2. Simpson’s Paradox 1198.3. Source of the Paradox 1218.4. Experimentation 1228.5. Randomization 1238.6. Exchangeability 1258.7. Spurious Association 1288.8. Independence 1308.9. Conclusions 1329. Variation 1349.1. Variation and Uncertainty 1349.2. Binomial Distribution 1359.3. Expectation 1379.4. Poisson Distribution 1399.5. Spread 1429.6. Variability as an Experimental Tool 1449.7. Probability and Chance 1459.8. Pictorial Representation 1479.9. The Normal Distribution 1509.10. Variation as a Natural Phenomenon 1529.11. Ellsberg’s Paradox 15410. Decision Analysis 158 10.1. Beliefs and Actions 15810.2. Comparison of Consequences 16010.3. Medical Example 16210.4. Maximization of Expected Utility 16410.5. More on Utility 16510.6. Some Complications 16710.7. Reason and Emotion 16810.8. Numeracy 17010.9. Expected Utility 17110.10. Decision Trees 17210.11. The Art and Science of Decision Analysis 17510.12. Further Complications 17710.13. Combination of Features 17910.14. Legal Applications 18211. Science 18611.1. Scientific Method 18611.2. Science and Education 18711.3. Data Uncertainty 18811.4. Theories 19011.5. Uncertainty of a Theory 19311.6. The Bayesian Development 19511.7. Modification of Theories 19711.8. Models 19911.9. Hypothesis Testing 20211.10. Significance Tests 20411.11. Repetition 20611.12. Summary 20812. Examples 21112.1. Introduction 21112.2. Cards 21212.3. The Three Doors 21312.4. The Newcomers to Your Street 21512.5. The Two Envelopes 21712.6. Y2K 22012.7. UFOs 22112.8. Conglomerability 22413. Probability Assessment 22613.1. Nonrepeatable Events 22613.2. Two Events 22713.3. Coherence 23013.4. Probabilistic Reasoning 23313.5. Trickle Down 23413.6. Summary 236Epilogue 238Subject Index 243Index of Examples 248Index of Notations 250