Lindley, Dennis V.
Understanding Uncertainty. - 2nd ed. - 1 online resource (299 pages) - Wiley Series in Probability and Statistics Ser. . - Wiley Series in Probability and Statistics Ser. .
Understanding Uncertainty -- Contents -- Preface -- Prologue -- Chapter 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 -- Chapter 2: Stylistic Questions -- 2.1. Reason -- 2.2. Unreason -- 2.3. Facts -- 2.4. Emotion -- 2.5. Normative and Descriptive Approaches -- 2.6. Simplicity -- 2.7. Mathematics -- 2.8. Writing -- 2.9. Mathematics Tutorial -- Chapter 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 -- Chapter 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 -- Chapter 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 -- 5.13. Closure -- Chapter 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 -- Chapter 7: Measuring Uncertainty -- 7.1. Classical Form -- 7.2. Frequency Data -- 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 -- Chapter 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 -- Chapter 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. Probability Densities -- 9.10. The Normal Distribution -- 9.11. Variation as a Natural Phenomenon -- 9.12. Ellsberg's Paradox -- Chapter 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 -- Chapter 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 -- Chapter 12: Examples -- 12.1. Introduction -- 12.2. Cards -- 12.3. The Three Doors -- 12.4. The Problem of Two Daughters -- 12.5. Two More Daughters and Cardano -- 12.6. The Two Envelopes -- 12.7. Y2K -- 12.8. UFOs -- 12.9. Conglomerability -- 12.10. Efron's Dice -- Chapter 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 -- Chapter 14: Statistics -- 14.1. Bayesian Statistics -- 14.2. A Bayesian Example -- 14.3. Frequency Statistics -- 14.4. Significance Tests -- 14.5. Betting -- 14.6. Finance -- Epilogue -- Subject Index -- Index of Examples -- Index of Notations.
Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty." -Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession A consideration of betting, showing that a bookmaker's odds are not expressions of probability Applications of the book's thesis to statistics A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.
9781118650233
Decision making -- Mathematics.
Mathematical statistics.
Probabilities.
Uncertainty -- Mathematics.
Electronic books.
QA273.L534 2013eb
519.2
Understanding Uncertainty. - 2nd ed. - 1 online resource (299 pages) - Wiley Series in Probability and Statistics Ser. . - Wiley Series in Probability and Statistics Ser. .
Understanding Uncertainty -- Contents -- Preface -- Prologue -- Chapter 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 -- Chapter 2: Stylistic Questions -- 2.1. Reason -- 2.2. Unreason -- 2.3. Facts -- 2.4. Emotion -- 2.5. Normative and Descriptive Approaches -- 2.6. Simplicity -- 2.7. Mathematics -- 2.8. Writing -- 2.9. Mathematics Tutorial -- Chapter 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 -- Chapter 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 -- Chapter 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 -- 5.13. Closure -- Chapter 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 -- Chapter 7: Measuring Uncertainty -- 7.1. Classical Form -- 7.2. Frequency Data -- 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 -- Chapter 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 -- Chapter 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. Probability Densities -- 9.10. The Normal Distribution -- 9.11. Variation as a Natural Phenomenon -- 9.12. Ellsberg's Paradox -- Chapter 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 -- Chapter 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 -- Chapter 12: Examples -- 12.1. Introduction -- 12.2. Cards -- 12.3. The Three Doors -- 12.4. The Problem of Two Daughters -- 12.5. Two More Daughters and Cardano -- 12.6. The Two Envelopes -- 12.7. Y2K -- 12.8. UFOs -- 12.9. Conglomerability -- 12.10. Efron's Dice -- Chapter 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 -- Chapter 14: Statistics -- 14.1. Bayesian Statistics -- 14.2. A Bayesian Example -- 14.3. Frequency Statistics -- 14.4. Significance Tests -- 14.5. Betting -- 14.6. Finance -- Epilogue -- Subject Index -- Index of Examples -- Index of Notations.
Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty." -Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession A consideration of betting, showing that a bookmaker's odds are not expressions of probability Applications of the book's thesis to statistics A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.
9781118650233
Decision making -- Mathematics.
Mathematical statistics.
Probabilities.
Uncertainty -- Mathematics.
Electronic books.
QA273.L534 2013eb
519.2