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Willful Ignorance: The Mismeasure of Uncertainty

Book Description

An original account of willful ignorance and how this principle relates to modern probability and statistical methods

Through a series of colorful stories about great thinkers and the problems they chose to solve, the author traces the historical evolution of probability and explains how statistical methods have helped to propel scientific research. However, the past success of statistics has depended on vast, deliberate simplifications amounting to willful ignorance, and this very success now threatens future advances in medicine, the social sciences, and other fields. Limitations of existing methods result in frequent reversals of scientific findings and recommendations, to the consternation of both scientists and the lay public.

Willful Ignorance: The Mismeasure of Uncertainty exposes the fallacy of regarding probability as the full measure of our uncertainty. The book explains how statistical methodology, though enormously productive and influential over the past century, is approaching a crisis. The deep and troubling divide between qualitative and quantitative modes of research, and between research and practice, are reflections of this underlying problem. The author outlines a path toward the re-engineering of data analysis to help close these gaps and accelerate scientific discovery.

Willful Ignorance: The Mismeasure of Uncertainty presents essential information and novel ideas that should be of interest to anyone concerned about the future of scientific research. The book is especially pertinent for professionals in statistics and related fields, including practicing and research clinicians, biomedical and social science researchers, business leaders, and policy-makers.

Table of Contents

  1. PREFACE
    1. NOTE
  2. ACKNOWLEDGMENTS
  3. 1 THE OPPOSITE OF CERTAINTY
    1. Two Dead Ends
    2. Analytical Engines
    3. What is Probability?
    4. Uncertainty
    5. Willful Ignorance
    6. Toward a New Science
    7. Notes
  4. 2 A QUIET REVOLUTION
    1. Thinking the Unthinkable
    2. Inventing Probability
    3. Statistics
    4. The Taming of Chance
    5. The Ignorance Fallacy
    6. The Dilemma of Science
    7. Notes
  5. 3 A MATTER OF CHANCE
    1. Origins
    2. The Famous Correspondence
    3. What Did Not Happen Next
    4. Against The Odds
    5. Notes
  6. 4 HARDLY TOUCHED UPON
    1. The Mathematics of Chance
    2. Empirical Frequencies
    3. A Quantum of Certainty
    4. Notes
  7. 5 A MATHEMATICIAN OF BASEL
    1. Publication at Last
    2. The Art of Conjecturing
    3. A Tragic Ending
    4. Notes
  8. 6 A DEFECT OF CHARACTER
    1. Man Without a Country
    2. A Fraction of Chances
    3. Notes
  9. 7 CLASSICAL PROBABILITY
    1. Revolutionary Reverends
    2. From Chances to Probability
    3. Notes
  10. 8 BABEL
    1. The Great Unraveling
    2. Probability as a Relative Frequency
    3. Probability as a Logical Relationship
    4. Probability as a Subjective Assessment
    5. Probability as a Propensity
    6. Notes
  11. 9 PROBABILITY AND REALITY
    1. The Razor's Edge
    2. What Fisher Knew
    3. What Reference Class?
    4. A Postulate of Ignorance
    5. Laplace's Error
    6. Notes
  12. 10 THE DECISION FACTORY
    1. Beyond Moral Certainty
    2. Decisions, Decisions
    3. Machine-Made Knowledge
    4. Notes
  13. 11 THE LOTTERY IN SCIENCE
    1. Scientific Progress
    2. Fooled by Causality
    3. Statistics for Humans: Bias or Ambiguity?
    4. Regression toward the Mean
    5. Notes
  14. 12 TRUST, BUT VERIFY
    1. A New Problem
    2. Trust, …
    3. … But Verify
    4. The Future
    5. Mindful Ignorance
    6. Notes
  15. APPENDIX: THE PASCAL–FERMAT CORRESPONDENCE OF 1654
    1. Notes
  16. BIBLIOGRAPHY
  17. INDEX
  18. END USER LICENSE AGREEMENT