Willful Ignorance The Mismeasure of Uncertainty

An original account ofwillful 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.

PREFACE xi

ACKNOWLEDGMENTS xv

1 THE OPPOSITE OF CERTAINTY 1

Two Dead Ends 2

Analytical Engines 4

What is Probability?  6

Uncertainty 9

Willful Ignorance 12

Toward a New Science 15

2 A QUIET REVOLUTION 19

Thinking the Unthinkable 21

Inventing Probability 24

Statistics 27

The Taming of Chance 31

The Ignorance Fallacy 34

The Dilemma of Science 35

3 A MATTER OF CHANCE 41

Origins 43

Probability 44

The Famous Correspondence 56

What Did Not Happen Next 60

AgainstThe Odds 64

4 HARDLY TOUCHED UPON 71

The Mathematics of Chance 73

Empirical Frequencies 82

A Quantum of Certainty 100

5 A MATHEMATICIAN OF BASEL 114

Publication at Last 116

The Art of Conjecturing 117

A Tragic Ending 142

6 A DEFECT OF CHARACTER 147

Man Without a Country 150

A Fraction of Chances 165

7 CLASSICAL PROBABILITY 171

Revolutionary Reverends 173

From Chances to Probability 194

8 BABEL 213

The Great Unraveling 216

Probability as a Relative Frequency 219

Probability as a Logical Relationship 228

Probability as a Subjective Assessment 239

Probability as a Propensity 247

9 PROBABILITY AND REALITY 253

The Razor’s Edge 255

What Fisher Knew 257

What Reference Class?  262

A Postulate of Ignorance 270

Laplace’s Error 279

10 THE DECISION FACTORY 283

Beyond Moral Certainty 284

Decisions, Decisions 298

Machine-Made Knowledge 309

11 THE LOTTERY IN SCIENCE 312

Scientific Progress 313

Fooled by Causality 319

Statistics for Humans: Bias or Ambiguity?  331

Regression toward the Mean 339

12 TRUST, BUT VERIFY 346

A New Problem 347

Trust,… 354

…But Verify 357

The Future 363

Mindful Ignorance 368

APPENDIX: THE PASCAL–FERMAT

CORRESPONDENCE OF 1654 373

NOTES 387

BIBLIOGRAPHY 415

INDEX 429 

Herbert I. Weisberg, PhD, is Founder of Causalytics, LLC, which develops innovative technology for predictive analytics for both medical research and business applications. He was previously President of Correlation Research Inc., a consulting firm specializing in the application of statistics to various business and legal issues. A Fellow of the American Statistical Association, Dr. Weisberg has published numerous articles and two previous books related to applied statistics.