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Understanding Uncertainty, Revised Edition

Book Description

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.

Table of Contents

  1. Cover
  2. Wiley Series in Probability and Statistics
  3. Title Page
  4. Copyright
  5. Preface
  6. Prologue
  7. Chapter 1: Uncertainty
    1. 1.1 Introduction
    2. 1.2 Examples
    3. 1.3 Suppression of Uncertainty
    4. 1.4 The Removal of Uncertainty
    5. 1.5 The Uses of Uncertainty
    6. 1.6 The Calculus of Uncertainty
    7. 1.7 Beliefs
    8. 1.8 Decision Analysis
  8. Chapter 2: Stylistic Questions
    1. 2.1 Reason
    2. 2.2 Unreason
    3. 2.3 Facts
    4. 2.4 Emotion
    5. 2.5 Normative and Descriptive Approaches
    6. 2.6 Simplicity
    7. 2.7 Mathematics
    8. 2.8 Writing
    9. 2.9 Mathematics Tutorial
  9. Chapter 3: Probability
    1. 3.1 Measurement
    2. 3.2 Randomness
    3. 3.3 A Standard for Probability
    4. 3.4 Probability
    5. 3.5 Coherence
    6. 3.6 Belief
    7. 3.7 Complementary Event
    8. 3.8 Odds
    9. 3.9 Knowledge Base
    10. 3.10 Examples
    11. 3.11 Retrospect
  10. Chapter 4: Two Events
    1. 4.1 Two Events
    2. 4.2 Conditional Probability
    3. 4.3 Independence
    4. 4.4 Association
    5. 4.5 Examples
    6. 4.6 Supposition and Fact
    7. 4.7 Seeing and Doing
  11. Chapter 5: The Rules of Probability
    1. 5.1 Combinations of Events
    2. 5.2 Addition Rule
    3. 5.3 Multiplication Rule
    4. 5.4 The Basic Rules
    5. 5.5 Examples
    6. 5.6 Extension of the Conversation
    7. 5.7 Dutch Books
    8. 5.8 Scoring Rules
    9. 5.9 Logic Again
    10. 5.10 Decision Analysis
    11. 5.11 The Prisoners' Dilemma
    12. 5.12 The Calculus and Reality
    13. 5.13 Closure
  12. Chapter 6: Bayes Rule
    1. 6.1 Transposed Conditionals
    2. 6.2 Learning
    3. 6.3 Bayes Rule
    4. 6.4 Medical Diagnosis
    5. 6.5 Odds Form of Bayes Rule
    6. 6.6 Forensic Evidence
    7. 6.7 Likelihood Ratio
    8. 6.8 Cromwell's Rule
    9. 6.9 A Tale of two Urns
    10. 6.10 Ravens
    11. 6.11 Diagnosis and Related Matters
    12. 6.12 Information
  13. Chapter 7: Measuring Uncertainty
    1. 7.1 Classical Form
    2. 7.2 Frequency Data
    3. 7.3 Exchangeability
    4. 7.4 Bernoulli Series
    5. 7.5 De Finetti's Result
    6. 7.6 Large Numbers
    7. 7.7 Belief and Frequency
    8. 7.8 Chance
  14. Chapter 8: Three Events
    1. 8.1 The Rules of Probability
    2. 8.2 Simpson's Paradox
    3. 8.3 Source of the Paradox
    4. 8.4 Experimentation
    5. 8.5 Randomization
    6. 8.6 Exchangeability
    7. 8.7 Spurious Association
    8. 8.8 Independence
    9. 8.9 Conclusions
  15. Chapter 9: Variation
    1. 9.1 Variation and Uncertainty
    2. 9.2 Binomial Distribution
    3. 9.3 Expectation
    4. 9.4 Poisson Distribution
    5. 9.5 Spread
    6. 9.6 Variability as an Experimental Tool
    7. 9.7 Probability and Chance
    8. 9.8 Pictorial Representation
    9. 9.9 Probability Densities
    10. 9.10 The Normal Distribution
    11. 9.11 Variation as a Natural Phenomenon
    12. 9.12 Ellsberg's Paradox
  16. Chapter 10: Decision Analysis
    1. 10.1 Beliefs and Actions
    2. 10.2 Comparison of Consequences
    3. 10.3 Medical Example
    4. 10.4 Maximization of Expected Utility
    5. 10.5 More on Utility
    6. 10.6 Some Complications
    7. 10.7 Reason and Emotion
    8. 10.8 Numeracy
    9. 10.9 Expected Utility
    10. 10.10 Decision Trees
    11. 10.11 The Art and Science of Decision Analysis
    12. 10.12 Further Complications
    13. 10.13 Combination of Features
    14. 10.14 Legal Applications
  17. Chapter 11: Science
    1. 11.1 Scientific Method
    2. 11.2 Science and Education
    3. 11.3 Data Uncertainty
    4. 11.4 Theories
    5. 11.5 Uncertainty of a Theory
    6. 11.6 The Bayesian Development
    7. 11.7 Modification of Theories
    8. 11.8 Models
    9. 11.9 Hypothesis Testing
    10. 11.10 Significance Tests
    11. 11.11 Repetition
    12. 11.12 Summary
  18. Chapter 12: Examples
    1. 12.1 Introduction
    2. 12.2 CARDS
    3. 12.3 The Three Doors
    4. 12.4 The Problem of Two Daughters
    5. 12.5 Two More Daughters and Cardano
    6. 12.6 The two Envelopes
    7. 12.7 Y2K
    8. 12.8 UFOs
    9. 12.9 Conglomerability
    10. 12.10 Efron's Dice
  19. Chapter 13: Probability Assessment
    1. 13.1 Nonrepeatable Events
    2. 13.2 Two Events
    3. 13.3 Coherence
    4. 13.4 Probabilistic Reasoning
    5. 13.5 Trickle Down
    6. 13.6 Summary
  20. Chapter 14: Statistics
    1. 14.1 Bayesian Statistics
    2. 14.2 A Bayesian Example
    3. 14.3 Frequency Statistics
    4. 14.4 Significance Tests
    5. 14.5 Betting
    6. 14.6 Finance
  21. Epilogue
  22. Subject Index
  23. Index of Examples
  24. Index of Notations