Prologue.

1. Uncertainty.

1.1. Introduction.

1.2. Examples.

1.3. Suppression of Uncertainty.

1.4. The Removal of Uncertainty.

1.5. The Uses of Uncertainty.

1.6. The Calculus of Uncertainty.

1.7. Beliefs.

1.8. Decision Analysis.

2. Stylistic Questions.

2.1. Reason.

2.2. Unreason.

Literature.

Advertising.

Politics.

Law.

Television.

2.3. Facts.

2.4. Emotion.

2.5. Prescriptive and Descriptive Approaches.

2.6. Simplicity.

2.7. Mathematics.

2.8. Writing.

2.9. Mathematics Tutorial.

3. Probability.

3.1. Measurement.

3.2. Randomness.

3.3. A Standard for Probability.

3.4. Probability.

3.5. Coherence.

3.6. Belief.

3.7. Complementary Event.

3.8. Odds.

3.9. Knowledge Base.

3.10. Examples.

3.11. Retrospect.

4. Two Events.

4.1. Two Events.

4.2. Conditional Probability.

4.3. Independence.

4.4. Association.

4.5. Examples.

4.6. Supposition and Fact.

4.7. Seeing and Doing.

5. The Rules of Probability.

5.1. Combinations of Events.

5.2. Addition Rule.

5.3. Multiplication Rule.

5.4. The Basic Rules.

5.5. Examples.

5.6. Extension of the Conversation.

5.7. Dutch Books.

5.8. Scoring Rules.

5.9. Logic Again.

5.10. Decision Analysis.

5.11. The Prisoners’ Dilemma.

5.12. The Calculus and Reality.

6. Bayes Rule.

6.1. Transposed Conditionals.

6.2. Learning.

6.3. Bayes Rule.

6.4. Medical Diagnosis.

6.5. Odds Form of Bayes Rule.

6.6. Forensic Evidence.

6.7. Likelihood Ratio.

6.8. Cromwell’s Rule.

6.9. A Tale of Two Urns.

6.10. Ravens.

6.11. Diagnosis and Related Matters.

6.12. Information.

7. Measuring Uncertainty.

7.1. Classical Form.

7.2. Frequency Data.3

7.3. Exchangeability.

7.4. Bernoulli Series.

7.5. De Finetti’s Result.

7.6. Large Numbers.

7.7. Belief and Frequency.

7.8. Chance.

8. Three Events.

8.1. The Rules of Probability.

8.2. Simpson’s Paradox.

8.3. Source of the Paradox.

8.4. Experimentation.

8.5. Randomization.

8.6. Exchangeability.

8.7. Spurious Association.

8.8. Independence.

8.9. Conclusions.

9. Variation.

9.1. Variation and Uncertainty.

9.2. Binomial Distribution.

9.3. Expectation.

9.4. Poisson Distribution.

9.5. Spread.

9.6. Variability as an Experimental Tool .

9.7. Probability and Chance.

9.8. Pictorial Representation.

9.9. The Normal Distribution.

9.10. Variation as a Natural Phenomenon.

9.11. Ellsberg’s Paradox.

10. Decision Analysis.

10.1. Beliefs and Actions.

10.2. Comparison of Consequences.

10.3. Medical Example.

10.4. Maximization of Expected Utility.

10.5. More on Utility.

10.6. Some Complications.

10.7. Reason and Emotion.

10.8. Numeracy.

10.9. Expected Utility.

10.10. Decision Trees.

10.11. The Art and Science of Decision Analysis.

10.12. Further Complications.

10.13. Combination of Features.

10.14. Legal Applications.

11. Science.

11.1. Scientific Method.

11.2. Science and Education.

11.3. Data Uncertainty.

11.4. Theories.

11.5. Uncertainty of a Theory.

11.6. The Bayesian Development.

11.7. Modification of Theories.

11.8. Models.

11.9. Hypothesis Testing.

11.10. Significance Tests.

11.11. Repetition.

11.12. Summary.

12. Examples.

12.1. Introduction.

12.2. Cards.

12.3. The Three Doors.

12.4. The Newcomers to Your Street.

12.5. The Two Envelopes.

12.6. Y2K.

12.7. UFOs.

12.8. Conglomerability.

13. Probability Assessment.

13.1. Nonrepeatable Events.

13.2. Two Events.

13.3. Coherence.

13.4. Probabilistic Reasoning.

13.5. Trickle Down.

13.6. Summary 236.

Epilogue.

Subject Index.

Index of Examples.

Index of Notations.