Skip to main content

Understanding Uncertainty

Understanding Uncertainty

Dennis V. Lindley

ISBN: 978-0-470-05548-9

Apr 2006

288 pages

Select type: O-Book

Description

A lively and informal introduction to the role of uncertainty and probability in people's lives from an everyday perspective

From television game shows and gambling techniques to weather forecasting and the financial markets, virtually every aspect of modern life involves situations in which the outcomes are uncertain and of varying qualities. But as noted statistician Dennis Lindley writes in this distinctive text, "We want you to face up to uncertainty, not hide it away under false concepts, but to understand it and, moreover, to use the recent discoveries so that you can act in the face of uncertainty more sensibly than would have been possible without the skill."

Accessibly written at an elementary level, this outstanding text examines uncertainty in various everyday situations and introduces readers to three rules--craftily laid out in the book--that prove uncertainty can be handled with as much confidence as ordinary logic. Combining a concept of utility with probability, the book insightfully demonstrates how uncertainty can be measured and used in everyday life, especially in decision-making and science.

With a focus on understanding and using probability calculations, Understanding Uncertainty demystifies probability and:
* Explains in straightforward detail the logic of uncertainty, its truths, and its falsehoods
* Explores what has been learned in the twentieth century about uncertainty
* Provides a logical, sensible method for acting in the face of uncertainty
* Presents vignettes of great discoveries made in the twentieth century
* Shows readers how to discern if another person--whether a lawyer, politician, scientist, or journalist--is talking sense, posing the right questions, or obtaining sound answers


Requiring only a basic understanding of mathematical concepts and operations, Understanding Uncertainty is useful as a text for all students who have probability or statistics as part of their course, even at the most introductory level.
Preface.

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.