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 by Sharon Bertsch McGrayne (PDF)

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A New York Times Book Review Editor’s Choice: A vivid account of the generations-long dispute over Bayes’ rule, one of the greatest breakthroughs in the history of applied mathematics and statistics”An intellectual romp touching on, among other topics, military ingenuity, the origins of modern epidemiology, and the theological foundation of modern mathematics.”—Michael Washburn, Boston Globe”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.”—David Robson, New Scientist 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 Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

User’s Reviews

Editorial Reviews: Review “If you’re not thinking like a Bayesian, perhaps you should be.”—John Allen Paulos, New York Times Book Review”A masterfully researched tale of human struggle and accomplishment . . . Renders perplexing mathematical debates digestible and vivid for even the most lay of audiences.”—Michael Washburn, Boston Globe”[An] engrossing study. . . . Her book is a compelling and entertaining fusion of history, theory and biography.”—Ian Critchley, Sunday Times”This account of how a once reviled theory, Baye’s rule, came to underpin modern life is both approachable and engrossing.”—Sunday Times”Makes the theory come alive . . . enjoyable . . . densely packed and engaging . . . very accessible . . . an admirable job of giving a voice to the scores of famous and non-famous people and data who contributed, for good or for worse.”—Significance Magazine”A very compelling documented account . . . very interesting reading.”—José Bernardo, Valencia List Blog”McGrayne explains [it] beautifully. . . . Top holiday reading.”—The Australian”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 statistics. I am confident that other readers will feel the same.”—The Lancet”A lively, engaging historical account. . . . McGrayne describes actuarial, business, and military uses of the Bayesian approach, including its application to settle the disputed authorship of 12 of the Federalist Papers, and its use to connect cigarette smoking and lung cancer. . . . All of this is accomplished through compelling, fast-moving prose. . . . The reader cannot help but enjoy learning about some of the more gossipy episodes and outsized personalities.”—Choice”Thorough research of the subject matter coupled with flowing prose, an impressive set of interviews with Bayesian statisticians, and an extremely engaging style in telling the personal stories of the few nonconformist heroes of the Bayesian school.”—Sam Behseta, Chance”A fascinating and engaging tale.”—Mathematical Association of America Reviews”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 American Mathematical Society “A very engaging book that statisticians, probabilists, and history buffs in the mathematical sciences should enjoy.”—David Agard, Cryptologia”Delightful . . . [and] McGrayne gives a superb synopsis of the fundamental development of probability and statistics by Laplace.”—Scott L. Zeger of Johns Hopkins, Physics Today”Superb.”—Andrew Hacker, New York Review of BooksEditor’s Choice, New York Times Book Review”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, University College London”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”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”Compelling, fast-paced reading full of lively characters and anecdotes . . . A great story.”—Robert E. Kass, Carnegie Mellon University”Fascinating . . . I truly admire [McGrayne’s] style of writing, and . . . ability to turn complex mathematical ideas into intriguing stories, centered around real people.”—Judea Pearl, winner of the 2012 Turing Award About the Author Sharon Bertsch McGrayne is the author of numerous books, including Nobel Prize Women in Science: Their Lives, Struggles, and Momentous Discoveries and Prometheans in the Lab: Chemistry and the Making of the Modern World. She lives in Seattle.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I like this book and enjoyed reading it, but kept feeling it would have benefited from some meatier examples, just as Sitting in Seattle indicated. I also felt that the author falsely equated Markov chains and Monte Carlo, and is a off on the role of simulation in statistics. Markov chains are certainly not things a frequentist statistician would have avoided even in the heyday of hardcore frequentism, or Bayes’ rule, for that matter. As a professor of mine, who was rather a committed anti-Bayesian once noted in class, being a committed Bayesian means always using Bayes’ rule. Simulation in statistics is older than MCMC by a long margin. In fact, W. S. Gossett made use of it in his original derivation of the t-distribution, which Fisher later put on sound analytic footing. Fisher also was a proponent of methods such as permutation, which have a simulation feel to them and weaken the assumptions of classical parametric statistics, but couldn’t realistically be implemented in the pre-computer era for anything but fairly small datasets. In more modern times, the workhorse of frequentist statistics is the simulation-based bootstrap, and foundations of that go back to the 1950s with techniques such as Quenouille’s jackknife (jackknife and bootstrap are both Tukey-isms). Even stalwart frequentist introduction to statistics books such as Hogg and Tanis’ Probability and Statistical Inference (which is now in many editions later than the one I used in my first statistics class way back when) mention it, and have some Bayes’ rule problems. Then there’s the famous RAND book 1,000,000 Random Digits, which proudly sat in the library of my graduate department, though of course no one consulted it anymore. I am also somewhat surprised not to see the work of Donald Rubin mentioned, or more on meta-analysis.All that aside, it’s a fun read and I recommend it to folks who want to know more, particularly those who know some statistics but not much about Bayesianism.Disclosure: I’m a psychometrician (statistician working in behavioral science) and consider myself a “pragmatic Bayesian”. I’ve used Bayesian techniques for some time now, and recommend them in many circumstances. In fact, in my field, Bayesian solutions have been used quite readily since the 1970s to handle some important but annoying technical issues that occur in practice, where imposing a bit of prior information often helps regularize problems to make them solvable, e.g., avoiding an inadmissible solution on a parameter that should be greater than 0. The psychometrics field made the transition to MCMC, at least in research, if not operationally, quite readily. Things are still really too complex for Joe/Josephine Average Behavioral Scientist to use, though that too is changing now that mainstream stat programs such as SAS are making Bayesian computation easier. Unfortunately the number of judgments for many scientists is simply too large for now, and I echo one of my colleagues (an expert in meta-analysis) in saying that without some care we might well be handing a loaded gun to folks who don’t know how to shoot.

⭐”The Theory That Would Not Die” is an enjoyable account of the history of Bayesian statistics from Thomas Bayes’s first idea to the ultimate (near-)triumph of Bayesian methods in modern statistics. As a statistically-oriented researcher and avowed Bayesian myself, I found that the book fills in details about the personalities, battles, and tempestuous history of the concepts.If you are generally familiar with the concept of Bayes’ rule and the fundamental technical debate with frequentist theory, then I can wholeheartedly recommend the book because it will deepen your understanding of the history. The main limitation occurs if you are *not* familiar with the statistical side of the debate but are a general popular science reader: the book refers obliquely to the fundamental problems but does not delve into enough technical depth to communicate the central elements of the debate.I think McGrayne should have used a chapter very early in the book to illustrate the technical difference between the two theories — not in terms of mathematics or detailed equations, but in terms of a practical question that would show how the Bayesian approach can answer questions that traditional statistics cannot. In many cases in McGrayne’s book, we find assertions that the Bayesian methods yielded better answers in one situation or another, but the underlying intuition about *why* or *how* is missing. The Bayesian literature is full of such examples that could be easily explained.A good example occurs on p. 1 of ET Jaynes’s Probability Theory: I observe someone climbing out a window in the middle of the night carrying a bag over the shoulder and running away. Question: is it likely that this person is a burgler? A traditional statistical analysis can give no answer, because no hypothesis can be rejected with observation of only one case. A Bayesian analysis, however, can use prior information (e.g., the prior knowledge that people rarely climb out wndows in the middle of the night) to yield both a technically correct answer and one that obviously is in better, common-sense alignment with the kinds of judgments we all make.If the present book included a bit more detail to show exactly how this occurs and why the difference arises, I think it would be substantially more powerful for a general audience.In conclusion: a good and entertaining book, although if you know nothing about the underlying debate, it may leave you wishing for more detail and concrete examples. If you already understand the technical side in some depth and can fill in the missing detail, then it will be purely enjoyable and you will learn much about the back history of the competing approaches to statistics.

⭐Whether or not you will enjoy this book depends on who you are. If you enjoy reading books about popular science, and trying to solve the occasional simple mathematical or logical puzzle, then you are ready for this one. If you want to understand the theory in any depth, or use it to solve problems, then you will need at least first-year undergraduate statistics to get started, much more to make progress -­ and a book with the formal mathematics, but begin with this one first to get a perspective on the field before going into detail.It is not obvious how you should use data to decide what to believe or how to act, and, as theories of statistics were developed, statisticians tried several different ways of thinking about data and the conclusions that could reasonably be drawn from them. Unfortunately the divisions of opinion (perhaps largely due to the personalities of the leading thinkers) resulted in acrimonious and inconclusive arguments.Thomas Bayes was a clergyman who died in 1761, leaving behind some mathematical papers. One of these was revised and corrected by Richard Price, so we don’t know quite what Bayes wrote or what he meant. This paper was the origin of two things: (1) the widely-used and uncontroversial `Bayes Theorem’, and (2) the controversial idea that probability could be expressed in terms of a measure of belief. In Bayesian statistics the researcher puts a belief into numerical terms and refines this belief in the light of subsequently observed data. The ‘subjective’ aspect of the theory brought it into disrepute, where it lingered for nearly 200 years. Many people faced with practical problems found that Bayesian methods worked, but either they didn’t know about Bayes or they preferred not to invite criticism by mentioning his name.In the last 60 years or so there has been a big revival in interest in Bayes theory, and it has been used to solve many problems that weren’t amenable to traditional methods. The big barrier was that some of the methods needed huge calculations, but with the availability of cheap, fast computers and new methods of calculation that barrier has almost disappeared.Sharon Bertsch Mcgrayne’s book gives a very clear and thorough history of “the theory that would not die.” As a practising statistician for more than 40 years I knew much of the published work that she has written about, and can vouch for her accuracy (there are a few corrections on her website), but until I read this book I did not have a clear idea of all of the historical developments and controversies. My only criticism is that the bibliography is organised by chapters, rather than as one alphabetically ordered sequence.

⭐Well first off, I’m delighted to see that co-founder Richard Price of Llangeinor is given proper credit. (Llangeinor in South Wales, is near where I live, But Rev Price did much more than re-write Rev Bayes’s notes)And I’m fascinated by the names of all the statisticians who I’d heard about, and a few I’ve even met (I taught stats at a midlands University).But having re-read it more closely, I now understand my quibbles: All Bayesians are treated as unsung heroes, the un-converted are knaves.For instance: p116 “Cornfield’s identification [in the Framingham study] in 1962 of the most critical risks factors [high cholesterol, high blood pressure] for cardiovascular disease produced….a dramatic drop in death rates from c.v. diease.”, because it seems that Cornfield used Bayes and the others didn’t.Now this is a complete travesty! Read Gary Taubes ‘The Diet Delusion’ and you’ll discover that poor analysis, and especially pre-conceptions meant that Framingham produced the ‘wrong’ results. Apart from smoking, none of the other factors matter. The low-fat obsession is making matters worse. A clear example of bad priors causing wrong posteriors?So did Cornfield and his bayesianism lead to these false conclusions? Ms. McGrayne, the author could be forgiven for not knowing this, but it shows how the book works — run with any ‘success’ for bayesianism (and ignore the failures?)Her attitude to my favourite statistician, Tukey is bizarre to say the least. She claims he did all sorts of secret work both for the military and for commercial clients that used Bayes, yet ignored his plain-sight comments that EDA — exploratory data analysis was what matters to most problem solvers; that CBA confirmatory data analysis was just an ornamental final flourish, and that was true for both bayesians and frequentists.[disclaimer: I wrote a book on EDA misleadingly titled ‘Mastering statistics with your micro-computer’ 1986]p 236 is to say the least, disingenuous! Greenspan, chairman of the Fed said in 2004 he used bayesian ideas to assess risk in financial policy. Ooops! He was proven spectacularly wrong by 2008! But Greenspan, claims Ms McGrayne didn’t do Bayes properly. ho! ho! pull the other one!This is a good book, well researched, and shines a light on otherwise neglected characters (statisticians, like me!). But she’s caught the bayesian bug in spades!

⭐This book seems to be not much more than an a promotional tract for Bayes . It depicts a series of situations where Bayes has been found useful, but nothing more than that. Do not expect anything which will help a beginner or anyone else to advance her or his understanding of the theorem or, or for the most part, even the simplest guidance as to how it might be applied in a practical situation.

⭐This riveting read deserves five stars because there are lots of books, papers, and websites about the maths of Bayes but this is the first really good description of the history and personalities involved. I think it’s great.If you’re interested in the maths it is perhaps best to look for original papers on the internet. I do know enough of the maths that I’m not frustrated, and I understand enough of the principles to know that the author has grasped them pretty well.I have books whose authors were just names to me before but now they are personalities. I have also been able to put things into a useful historical context and see how the events described in the book have an influence even now.Some of them actually happened within my lifetime and remind me of the intolerant git who presented the course on statistics within my psychology degree course.

⭐Very well written book – well structured, entertaining and researched. A useful introduction to Bayes theorem and application.But it’s just a little too much about the history of classic statistics vs pragmatic (Bayes) practicioners. And some of the history is very recent – the disagreements over the different approaches still going into the 1990s – though I do now feel the need to double check this schism against other sources.Rather too little on the mathematics. The basic concept is easy and well covered enough in the Appendix giving some worked examples, but there is clearly much more to it that that eg MCMC. At some point I’ll want to have a play with WinBUGS.

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