The theory that would not die: how bayes’ rule cracked the enigma code, hunted down russian submarines, & emerged triumphant from two centuries of controversy

335 Pages·2011·2.64 MB·English

by  Sharon Bertsch

the theory that would not die
other books by
sharon bertsch mcgrayne
Prometheans in the Lab: Chemistry and the Making
of the Modern World
Iron, Nature’s Universal Element: Why People Need
Iron and Animals Make Magnets (with Eugenie V.
Mielczarek)
Nobel Prize Women in Science: Their Lives, Struggles,
and Momentous Discoveries
the theory
that would
not die
how bayes’ rule cracked
the enigma code,
hunted down russian
submarines, & emerged
triumphant from two
centuries of controversy
sharon bertsch mcgrayne
new haven & london
“The Doctor sees the light” by Michael Campbell is reproduced by permission of John Wiley &
Sons; the lyrics by George E. P. Box in chapter 10 are reproduced by permission of John Wiley &
Sons; the conversation between Sir Harold Jeffreys and D. V. Lindley in chapter 3 is reproduced
by permission of the Master and Fellows of St. John’s College, Cambridge.
Copyright © 2011 by Sharon Bertsch McGrayne. All rights reserved. This book may not be repro-
duced, in whole or in part, including illustrations, in any form (beyond that copying permitted
by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press),
without written permission from the publishers.
Yale University Press books may be purchased in quantity for educational, business, or promo-
tional use. For information, please e- mail [email protected] (U.S. office) or [email protected]
.uk (U.K. office).
Designed by Lindsey Voskowsky. Set in Monotype Joanna type by Duke & Company, Devon,
Pennsylvania. Printed in the United States of America.
Library of Congress Cataloging-in-Publication Data
McGrayne, Sharon Bertsch.
The theory that would not die : how Bayes’ rule cracked the enigma code, hunted down Rus-
sian submarines, and emerged triumphant from two centuries of controversy / Sharon Bertsch
McGrayne.
p. cm.
Summary: “Bayes’ rule appears to be a straightforward, one-line theorem: by updating our
initial beliefs with objective new information, we get a new and improved belief. To its adher-
ents, it is an elegant statement about learning from experience. To its opponents, it is subjec-
tivity run amok. In the first-ever account of Bayes’ rule for general readers, Sharon Bertsch
McGrayne explores this controversial theorem and the human obsessions surrounding it. She
traces its discovery by an amateur mathematician in the 1740s through its development into
roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected
statisticians rendered it professionally taboo for 150 years—at the same time that practitioners
relied on it to solve crises involving great uncertainty and scanty information, even breaking
Germany’s Enigma code during World War II, and explains how the advent of off-the-shelf
computer technology in the 1980s proved to be a game-changer. Today, Bayes’ rule is used
every where from DNA de-coding to Homeland Security. Drawing on primary source material
and interviews with statisticians and other scientists, The Theory That Would Not Die is the
riveting account of how a seemingly simple theorem ignited one of the greatest controversies
of all time”—Provided by publisher.
Includes bibliographical references and index.
ISBN 978-0-300-16969-0 (hardback)
1. Bayesian statistical decision theory—History. I. Title.
QA279.5.M415 2011
519.5 ′42—dc22
2010045037
A catalogue record for this book is available from the British Library.
This paper meets the requirements of ANSI/NISO Z39.48–1992 (Permanence of Paper).
10 9 8 7 6 5 4 3 2 1
When the facts change, I change my opinion. What do you do, sir?
—John Maynard Keynes

contents
Preface and Note to Readers ix
Acknowledgments xii
Part I. Enlightenment and the Anti- Bayesian Reaction 1
1. Causes in the Air 3
2. The Man Who Did Everything 13
3. Many Doubts, Few Defenders 34
Part II. Second World War Era 59
4. Bayes Goes to War 61
5. Dead and Buried Again 87
Part III. The Glorious Revival 89
6. Arthur Bailey 91
7. From Tool to Theology 97
8. Jerome Cornfield, Lung Cancer, and Heart Attacks 108
9. There’s Always a First Time 119
10. 46,656 Varieties 129
Part IV. To Prove Its Worth 137
11. Business Decisions 139
12. Who Wrote The Federalist? 154
13. The Cold Warrior 163
14. Three Mile Island 176
15. The Navy Searches 182
viii Contents
Part V. Victory 211
16. Eureka! 213
17. Rosetta Stones 233
Appendixes 253
Dr. Fisher’s Casebook 253
Applying Bayes’ Rule to Mammograms and Breast Cancer 255
Notes 259
Glossary 271
Bibliography 275
Index 307
preface and
note to readers
In a celebrated example of science gone awry, geologists accumulated the
evidence for Continental Drift in 1912 and then spent 50 years arguing that
continents cannot move.
The scientific battle over Bayes’ rule is less well known but lasted far
longer, for 150 years. It concerned a broader and more fundamental issue:
how we analyze evidence, change our minds as we get new information, and
make rational decisions in the face of uncertainty. And it was not resolved
until the dawn of the twenty- first century.
On its face Bayes’ rule is a simple, one- line theorem: by updating our
initial belief about something with objective new information, we get a new
and improved belief. To its adherents, this is an elegant statement about
learning from experience. Generations of converts remember experiencing
an almost religious epiphany as they fell under the spell of its inner logic.
Opponents, meanwhile, regarded Bayes’ rule as subjectivity run amok.
Bayes’ rule began life amid an inflammatory religious controversy in
England in the 1740s: can we make rational conclusions about God based
on evidence about the world around us? An amateur mathematician, the
Reverend Thomas Bayes, discovered the rule, and we celebrate him today
as the iconic father of mathematical decision making. Yet Bayes consigned
his discovery to oblivion. In his time, he was a minor figure. And we know
about his work today only because of his friend and editor Richard Price, an
almost forgotten hero of the American Revolution.
By rights, Bayes’ rule should be named for someone else: a French-
man, Pierre Simon Laplace, one of the most powerful mathematicians and
ix