The Theory That Would Not Die

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

Sharon Bertsch Mcgrayne
Copyright Date: 2011
Published by: Yale University Press
Pages: 288
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  • Book Info
    The Theory That Would Not Die
    Book Description:

    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 adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity 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 (Alan Turing's role in 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 everywhere from DNA de-coding to Homeland Security.

    Drawing on primary source material and interviews with statisticians and other scientists,The Theory That Would Not Dieis the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    eISBN: 978-0-300-17509-7
    Subjects: History of Science & Technology, Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. Preface and Note to Readers
    (pp. ix-xi)
  4. Acknowledgments
    (pp. xii-xiv)
  5. Part I. Enlightenment and the Anti-Bayesian Reaction
    • 1. Causes in the Air
      (pp. 3-12)

      Sometime during the 1740s, the Reverend Thomas Bayes made the ingenious discovery that bears his name but then mysteriously abandoned it. It was rediscovered independently by a different and far more renowned man, Pierre Simon Laplace, who gave it its modern mathematical form and scientific application—and then moved on to other methods. Although Bayes’ rule drew the attention of the greatest statisticians of the twentieth century, some of them vilified both the method and its adherents, crushed it, and declared it dead. Yet at the same time, it solved practical questions that were unanswerable by any other means: the...

    • 2. The Man Who Did Everything
      (pp. 13-33)

      Just across the English Channel from Tunbridge Wells, about the time that Thomas Bayes was imagining his perfectly smooth table, the mayor of a tiny village in Normandy was celebrating the birth of a son, Pierre Simon Laplace, the future Einstein of his age.

      Pierre Simon, born on March 23, 1749, and baptized two days later, came from several generations of literate and respected dignitaries. His mother’s relatives were well-to-do farmers, but she died when he was young, and he never referred to her. His father kept the stagecoach inn in picturesque Beaumonten-Auge, was a leader of the community’s 472...

    • 3. Many Doubts, Few Defenders
      (pp. 34-58)

      With Laplace gone, Bayes’ rule entered a tumultuous period when it was disdained, reformed, grudgingly tolerated, and finally nearly obliterated by battling theorists. Yet through it all the rule chugged sturdily along, helping to resolve practical problems involving the military, communications, social welfare, and medicine in the United States and Europe.

      The backdrop to the drama was a set of unsubstantiated but widely circulated charges against Laplace’s reputation. The English mathematician Augustus de Morgan wrote inThe Penny Cyclopaediaof 1839 that Laplace failed to credit the work of others; the accusation was repeated without substantiation for 150 years until...

  6. Part II. Second World War Era
    • 4. Bayes Goes to War
      (pp. 61-86)

      By 1939 Bayes’ rule was virtually taboo, dead and buried as far as statisticians in the know were concerned. A disturbing question remained, though. How could wartime leaders make the best possible life-and-death decisions swiftly, without waiting for complete information? In deepest secrecy some of the greatest mathematical minds of the century would contribute to rethinking Bayes’ role during the uncertain years ahead.

      The U-boat peril was the only thing that ever really frightened Winston Churchill during the Second World War, he recalled in his history of the conflict. Britain was self-sufficient in little other than coal; it grew enough...

    • 5. Dead and Buried Again
      (pp. 87-88)

      With its wartime successes classified, Bayes’ rule emerged from the Second World War even more suspect than before. Statistics books and papers stressed repeatedly and self-righteously that they did not use the rule. When Jack Good discussed the method at the Royal Statistical Society, the next speaker’s opening words were, “After that nonsense …”¹

      “Bayes” still meant equal priors and did not yet mean making inferences, conclusions, or predictions based on updating observational data. The National Bureau of Standards suppressed a report to Aberdeen Proving Ground, the U.S. Army’s weapons-testing center, during the 1950s because the study used subjective Bayesian...

  7. Part III. The Glorious Revival
    • 6. Arthur Bailey
      (pp. 91-96)

      After the Second World War the first public challenge to the anti-Bayesian status quo came not from the military or university mathematicians and statisticians but from a Bible-quoting business executive named Arthur L. Bailey.

      Bailey was an insurance actuary whose father had been fired and blackballed by every bank in Boston for telling his employers they should not be lending large sums of money to local politicians. So ostracized was the family that even Arthur’s schoolmates stopped inviting him and his sister to parties. Turning his back on the New England establishment, Bailey enrolled at the University of Michigan in...

    • 7. From Tool to Theology
      (pp. 97-107)

      While Arthur Bailey was transforming the sledgehammer of Credibility into Bayes’ rule for the insurance industry, a postwar boom in statistics was elevating the method’s lowly status. Gradually, Bayes would shed its reputation as a mere tool for solving practical problems and emerge in glorious Technicolor as an all-encompassing philosophy. Some would even call it a theology.

      The Second World War had radically upgraded the stature, financial prospects, and career opportunities of applied mathematicians in the United States. The military was profoundly impressed by its wartime experience with statistics and operations research, and during the late 1940s the government poured...

    • 8. Jerome Cornfield, Lung Cancer, and Heart Attacks
      (pp. 108-118)

      Bayes came to medical research through the efforts of a single scientist, Jerome Cornfield, whose only degree was a B.A. in history and who relied on the rule to identify the causes of lung cancer and heart attacks.

      Lung cancer, extremely rare before 1900 and still uncommon in 1930, sprang up as if out of nowhere shortly after the Second World War. By 1952 it was killing 321 people per million per year in England and Wales. A year later approximately 30,000 new cases were diagnosed in the United States. No other form of cancer showed such a catastrophic leap....

    • 9. There’s Always a First Time
      (pp. 119-128)

      Bayes’ military successes were still Cold War secrets when Jimmie Savage visited the glamorous new RAND Corporation in the summer of 1957 and encouraged two young men to calculate a life-and-death problem: the probability that a thermonuclear bomb might explode by mistake.

      RAND was the quintessential Cold War think tank. Gen. Curtis E. LeMay, the commander of the Strategic Air Command (SAC), had helped start it in Santa Monica, California, 10 years earlier as “a gimmick” to cajole top scientists into applying operations research to long-range air warfare.¹ But RAND, an acronym for Research ANd Development, considered itself a “university...

    • 10. 46,656 Varieties
      (pp. 129-136)

      In sharp contrast to the super secrecy of Madansky’s H-bomb report, the schism between entrenched frequentists and upstart Bayesians was getting downright noisy. As usual, the bone of contention was the subjectivity of Thomas Bayes’ pesky prior. The idea of importing knowledge that did not originate in the statistical data at hand was anathema to the anti-Bayesian duo Fisher and Neyman. Since they were making conclusions and predictions about data without using prior odds, Bayesian theoreticians on the defensive struggled to avoid priors altogether.

      Bayesian theories mushroomed in glorious profusion during the 1960s, and Jack Good claimed he counted “at...

  8. Part IV. To Prove Its Worth
    • 11. Business Decisions
      (pp. 139-153)

      With new statistical theories cropping up almost daily during the 1960s, the paltry number of practical applications in the public arena was becoming a professional embarrassment.

      Harvard’s John W. Pratt complained that Bayesians and frequentists alike were publishing “too many minor advances extracted from real or mythical problems, sanitized, rigorized, polished, and presented in pristine mathematical form and multiple forums.”¹

      Bayesians in particular seemed unwilling to apply their theories to real problems. Savage’s rabbit ears and 20-pound chairs were textbook showpieces, even less substantial than Egon Pearson’s chestnut foals and pipe-smoking males of 30 years before. They were “dumb,” a...

    • 12. Who Wrote The Federalist?
      (pp. 154-162)

      Alfred C. Kinsey’s explosive bestsellerSexual Behavior in the Human Malewas published in 1948, the same year pollsters failed to predict Harry Truman’s victory over Thomas Dewey in the presidential election. With the public crying foul, fraud, and debauchery, social scientists feared for the future of their profession. Opinion polling was one of their basic tools, so the Social Science Research Council, representing seven professional societies, appointed statistician Frederick Mosteller of Harvard University to investigate the scandals.

      Mosteller’s forthright report on Truman’s election blamed the nation’s pollsters for rejecting randomized sampling and for clinging to outdated sampling designs that...

    • 13. The Cold Warrior
      (pp. 163-175)

      The Federalistproject impressed the still small world of professional statisticians, but John Tukey, a star from the world of Cold War spying, would give Bayes’ rule the opportunity to demonstrate its prowess before 20 million American television viewers. But would the statistical community learn from Tukey’s example that Bayes had come of age? That was the question.

      Bayes’ big chance at fame commenced in 1960 with the race between Senator Kennedy and Vice President Richard M. Nixon to succeed Eisenhower as president. The election was far too close to call, but the nation’s three major television networks competed fiercely...

    • 14. Three Mile Island
      (pp. 176-181)

      After years of working together, the two old friends Fred Mosteller and John Tukey reminisced in 1967 about how “the battle of Bayes has raged for more than two centuries, sometimes violently, sometimes almost placidly, … a combination of doubt and vigor.” Thomas Bayes had turned his back on his own creation; a quarter century later, Laplace glorified it. During the 1800s it was both employed and undermined. Derided during the early 1900s, it was used in desperate secrecy during the Second World War and afterward employed with both astonishing vigor and condescension.¹ But by the 1970s Bayes’ rule was...

    • 15. The Navy Searches
      (pp. 182-210)

      Surprisingly, given Bayes’ success in fighting U-boats during the Second World War, the U.S. Navy embraced the method slowly and grudgingly during the Cold War. High-ranking officers turned to Bayes almost accidentally, hoping at first to garner only the trappings of statistics. Later, the navy would move with increasing confidence and growing computer power to fine-tune the method for antisubmarine warfare. Meanwhile, the Coast Guard eyed the method for rescuing people lost at sea. As was often the case with Bayes’ rule, a series of spectacular emergencies forced the issue. The navy’s flirtation with the approach began at dusk on...

  9. Part V. Victory
    • 16. Eureka!
      (pp. 213-232)

      As the computer revolution flooded the modern world with data, Bayes’ rule faced one of its biggest crises in 250 years. Was an eighteenth-century theory—discovered when statistical facts were scarce and computation was slow and laborious—doomed to oblivion? It had already survived five nearfatal blows: Bayes had shelved it; Price published it but was ignored; Laplace discovered his own version but later favored his frequency theory; frequentists virtually banned it; and the military kept it secret.

      By 1980 anyone studying the environment, economics, health, education, or social science was tap-tapping data into a terminal connected to a mainframe...

    • 17. Rosetta Stones
      (pp. 233-252)

      Two and a half centuries after Bayes and Laplace discovered a way to apply mathematical reasoning to highly uncertain situations, their method has taken wing, soaring through science and the Internet, burrowing into our daily lives, dissolving language barriers, and perhaps even explaining our brains. Gone are the days when a few driven individuals searched orphanages and coded messages for data and organized armies of women and students to make tedious calculations. Today’s Bayesians revel in vast archives of Internet data, off-the-shelf software, tools like MCMC, and computing power so cheap it is basically free.

      The battle between Bayesian and...

  10. Appendix A Dr Fisher’s Casebook: The Doctor Sees The Light
    (pp. 253-254)
    Michael j. Campbell
  11. Appendix B Applying Bayes’ Rule to Mammograms and Breast Cancer
    (pp. 255-258)
  12. Notes
    (pp. 259-270)
  13. Glossary
    (pp. 271-274)
  14. Bibliography
    (pp. 275-306)
  15. Index
    (pp. 307-320)