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The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy.

In the first-ever account of Bayes’ rule for general readers, Sharon Bertsch McGrayne explores the controversies and human obsessions surrounding it. She traces its discovery by the amateur mathematician Reverend Bayes in the 1740s through its development into roughly its modern form by the great French scientist Pierre Simon Laplace. She reveals why respected academics rendered it professionally taboo for decades – while decision-makers relied on it to solve crises involving great uncertainty and scanty information. A prime example is how Alan Turing used Bayes to break the German U-boats’ Enigma code during World War II. She also explains how the advent of off-the-shelf computer technology in the 1980s was a game-changer. Today, Bayes’ rule is used everywhere, from DNA decoding to Homeland Security.

Drawing on primary source material and interviews with scores of statisticians and 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.

German (Springer Verlag), Japanese, Korean, and Spanish translations.

Praise from Reviewers

"If you are not thinking like a Bayesian, perhaps you should be."

—John Allen Paulos, New York Times Book Review.

Editor's Choice, New York Times Book Review.
“I recently finished reading The Theory That Would Not Die. … Bayes’s rule is a statistical theory that has a long and interesting history. It is important in decision making — how tightly should you hold on to your view and how much should you update your view based on the new information that’s coming in. We intuitively use Bayes’s rule every day…"
—Alan B. Krueger, chairman of President Obama’s Council of Economic Advisers. in Jan. 1, 2012, New York Times.

"A rollicking tale of the triumph of a powerful mathematical tool... Impressively researched."

"Carefully balanced to be accessible to a lay audience while captivating to a statistical one. Told without formulas, this eloquently written story is the history of an idea."

—Andrew Hacker, The New York Review of Books.

“A ‘find.’ … For the student who is being exposed to Bayesian statistics for the first time, McGrayne’s book provides a wealth of illustrations to whet his or her appetite for more. It will broaden and deepen the field of reference of the more expert statistician, and the general reader will find an understandable, well-written, and fascinating account of a scientific field of great importance today.”
— Andrew I. Dale, Notices of the AMS

Recommended summer reading.
— Business Week

"Marvelous book. ... McGrayne has transformed the tale of Bayes into a page-turning potboiler. We can not recommend it too highly."
—Howard Wainer and Sam Savage, Journal of Educational Measurement.

"A delightful change of pace from more technical historical accounts ... McGrayne gives a superb synopsis of the fundamental development of probability and statistics by Laplace."
—Physics Today

"An example of the best in historical scientific journalism: it captures the main threads of the science while going much further on the human side of the story... This is a remarkable achievement. It taught me things, and it made me think. ... This book succeeds gloriously, by never losing sight of the story, and it's a wonderful story, one that desperately deserved to be told."
—Robert E. Kass, Carnegie Mellon University

"McGrayne is such a good writer that she makes this obscure battle gripping for the general reader. ... [She writes] with great clarity and wit.”
—Engineering and Technology Magazine.

McGrayne ... articulates difficult ideas in a way that the general public can understand and appreciate. ... I highly recommend it to anyone interested in science, history, and the evolution of a theorem over time. The book read as if it were a love story — for an algorithm that grew up neglected, periodically taken out for a ride but mostly sitting home alone, until at long last, it finally found its rightful place of respect and appreciation in the world."
—IEEE Computing Now.

"A Statistical Thriller... McGrayne's tale has everything you would expect of a modern-day thriller. Espionage, nuclear warfare and cold war paranoia all feature... a host of colourful characters and their bitter rivalries carry the tale... McGrayne's writing is luminous. ... To have crafted a page-turner out of the history of statistics is an impressive feat. If only lectures at university had been this racy."
— NewScientist

"A compelling and entertaining fusion of history, theory and biography... McGrayne is adept at explaining abstruse mathematics in layperson's language."
— Sunday Times

"Approachable and engrossing. ... One of the 100 best holiday reads."
— Sunday Times

"An intellectual romp ... a masterfully researched tale of human struggle and accomplishment, and it renders perplexing mathematical debates digestible and vivid for even the most lay of audiences. Acknowledging ignorance is the first step toward knowledge, yes, and when we wed our ignorance with our better instincts we often find the best possible second step."
— The Boston Globe

"The book is very non-technical ... yet the reasoning behind the Rule resonates throughout. ... A very engaging book that statisticians, probabilists, and history buffs in the mathematical sciences should enjoy."

"A fascinating and engaging tale."
—Mathematical Association of American Reviews

“A masterpiece and an invaluable contribution to the scientific literature, in general, and the actuarial literature in particular. The book is a treasure trove of citations to interesting items in the literature and biographical information on key figures in Bayesian history that we found extremely difficult to find prior to the arrival of this book.”
— Tom Herzog, Expanding Horizons, Society of Actuaries

"A book simply highlighting the astonishing 200 year controversy over Bayesian analysis would have been highly welcome. This book does so much more, however, uncovering the almost secret role of Bayesian analysis in a stunning series of the most important developments of the twentieth century. What a revelation and what a delightful read!"

—James Berger, Arts & Sciences Professor of Statistics, Duke University, and member, National Academy of Sciences

"Engrossing ... a flair for bringing to life the often eccentric personalities... a compelling and entertaining fusion of history, theory and biography ... adept at explaining abstruse mathematics in layperson's language"
—The London Times

“We now know how to think rationally about our uncertain world. This book describes in vivid prose, accessible to the lay person, the development of Bayes' rule over more than two hundred years from an idea to its widespread acceptance in practice.”
—Dennis Lindley, author of Understanding Uncertainty

"Many gripping and occasionally startling stories that grace Sharon Bertsch McGrayne's highly enjoyable new history of Bayesian inference. ... Actuaries play a particular notable role in McGrayne's hidden history of 20th century Bayes."

“Well known in statistical circles, Bayes’s Theorem was first given in a posthumous paper by the English clergyman Thomas Bayes in the mid-eighteenth century. McGrayne provides a fascinating account of the modern use of this result in matters as diverse as cryptography, assurance, the investigation of the connection between smoking and cancer, RAND, the identification of the author of certain papers in The Federalist, election forecasting and the search for a missing H-bomb. The general reader will enjoy her easy style and the way in which she has successfully illustrated the use of a result of prime importance in scientific work.”
—Andrew I. Dale, author of A History of Inverse Probability From Thomas Bayes to Karl Pearson and Most Honorable Remembrance: The Life and Work of Thomas Bayes

"Very compelling, ... very interesting reading."
–Jose Bernardo, Valencia List

"Makes the theory come alive, ... gives a voice to the scores of famous and non-famous people and data who contributed, for good or for worse."
Significance Magazine

"Lively, engaging historical account... Compelling, fast-moving prose. ... Recommended."

"Engaging. ... Readers will be amazed at the impact that Bayes' rule has had in diverse fields, as well as by its rejection by too many statisticians. ... I was brought up, statistically speaking, as what is called a frequentist... But reading McGrayne's book has made me determined to try, once again, to master the intricacies of Bayesian statisics. I am confident that other readers will feel the same."
The Lancet

Wiskunde die je laat leren van je onwetendheid.
—NRC Handelsblad.

"McGrayne's book is not a textbook and does not attempt to teach Bayesian inferential techniques. Rather, McGrayne offers a very thorough, informative, and often entertaining (in our humble opinion) discussion of the Bayesian perspective... Strongly recommended [for students] as it provides the theoretical underpinnings of the Bayesian perspective and shows how Bayesianism has been applied to real world inferential / statistical problems."
— Jon Starkweather, RSS Matters.

"McGrayne explains [it] beautifully. ... Top holiday reading."
—The Australian

I would like to thank several readers who alerted me to typographical errors, which have been corrected in reprintings.

On pages 78 and 79, references to a circle 236 miles across should be changed to a rectangle measuring 50 x 200 miles, that is, to an area of 10,000 square miles. Alan Chodos spotted this one.

Page 131, line 19: both the first y and the third y in the James-Stein formula should have a bar on top. A kind reader known to me only as Richard pointed this problem out to me.

Page 191, line 11 from the bottom: change "32 kilobytes" to "32K words." During the 1960s, as "David" kindly reminded me, words were the unit of measurement for computer memory.

Page 256 and 257, the numbers 32/10,000 should be 32/40. The error does not affect the answer. Preston Gardner, Kevin Murphy, and William Benitz, MD., alerted me to this.