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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

Sharon Bertsch McGrayne

3.75 · Rating details · 2,264 ratings · 287 reviews

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 explo ...more

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Hardcover, 336 pages

Published May 17th 2011 by Yale University Press (first published May 14th 2011)

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Sep 03, 2012 rmn rated it it was ok

Shelves: financial-math-non-fiction

If only I had known how to use Bayesian probabilities before reading this book I could have taken the probability of my liking a book well received in a NY Times Book Review as my prior, plugged that in to a Bayesian calculation as to whether or not I would like this book, and quickly would have come up with the answer "highly unlikely" and saved myself a few hours of my life.

According to the author, Bayes' rule is the greatest mathematical equation/formula/thought process in the history of hist If only I had known how to use Bayesian probabilities before reading this book I could have taken the probability of my liking a book well received in a NY Times Book Review as my prior, plugged that in to a Bayesian calculation as to whether or not I would like this book, and quickly would have come up with the answer "highly unlikely" and saved myself a few hours of my life.

According to the author, Bayes' rule is the greatest mathematical equation/formula/thought process in the history of history and can solve any problem from finding a lost submarine, to determining who really wrote which Federalist Paper, to figuring out why people like country music (ok, I made the last one up because you don't need an equation to come up with the answer "insanity"). Anyway, the annoyance of this book is the author pontificates on how great Bayes' Rule is without ever, you know, actually giving us a mathematical example. It's mindblowingly frustrating.

The chapters basically read like this. The British government wanted to crack the Nazi Enigma code in WWII so they hired Alan Turing who employed Bayes' Rule, and voila! Problem solved. Or, the US wanted to find a missing submarine so they used Bayes' Rule and there it was.

Bayes' Rule could have been anything. The fact that the author does such a poor job of defining it and a poorer job of showing how it was actually used and some of the math behind it is irritating. You could find and replace "Bayes' Rule" with "Johnson Rod" throughout the whole book and not lose anything. By keeping Bayes' Rule essentially as a black box, it becomes less interesting overall.

There was an attempt in the appendix to show a simple mathematical application of Bayes' Rule, which was helpful, but even that was screwed up as the verbal description of the variables did not match the equation (numerators were flip-flopped on consecutive pages, doesn't change the outcome, but come on, you need consistency when showing the formula about which the entire book is written).

The history of Bayes' Rule is really what the book is about, and some of it is entertaining, but save yourself some time and just wikipedia it and you'll learn infinitely more in a shorter period of time. ...more

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May 21, 2011 David Rubenstein rated it really liked it

Shelves: history, technology, mathematics

I think this is the first book about Bayes' theorem and its applications, for the general reader. The book does not explicitly state the theorem as a mathematical formula, until the second appendix. However, the general idea is described, as well the general ideas behind it. The history of the theorem is described in some detail.

The ebb and flow in belief in the theorem over the course of 150 years is interesting. Applying Bayes theorem requires a prior probability, and this is often poorly know ...more

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Oct 08, 2011 Michael rated it it was ok

As someone who actually works with Bayesian methods, I was very much looking forward to reading this book. The strange history of Bayes' Theorem had been briefly mentioned in other, more technical books I had read. I finally wanted to get the whole story.

Alas, that story, at least as presented in this book, turned out to be not quite so exciting. Except for the insights into Laplace's involvement, and in particular the interesting sections on Alan Turing's work, I found this to be a rather lifel ...more

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Nov 30, 2015 Charlene rated it really liked it

Shelves: decision-making, constructs, biography, innovation, general-science

This was an excellent biography of Bayes' Rule, which basically glossed over Bayes himself. The author chose instead to examine the lesser known scientists and applications associated with Bayes. As a result, after reading this you are likely to call Bayes' Rule BLP Rule, for Bayes-Laplace Rule. The author was most interested in highlighting the work done by Pierre-Simone Laplace, who I feel I have come to know so much more after this biography. Prior to this book, Laplace came on my radar after This was an excellent biography of Bayes' Rule, which basically glossed over Bayes himself. The author chose instead to examine the lesser known scientists and applications associated with Bayes. As a result, after reading this you are likely to call Bayes' Rule BLP Rule, for Bayes-Laplace Rule. The author was most interested in highlighting the work done by Pierre-Simone Laplace, who I feel I have come to know so much more after this biography. Prior to this book, Laplace came on my radar after watching a Sean Carroll talk , listening toFrederick Gregory's lecture series, History of Science 1700 - 1900, and reading David Bodanis' e=mc2. (My memory indicated Bodanis included Laplace in his book, but attempts to confirm this have not been successful. Maybe credit is due another author. It is possible I have oddly attributed my knowledge of Laplace to someone who didn't even include him a book. Memory is so strange.).

I remember being a bit wowed and intrigued after first learning about Laplace; and yet, not doing any further research. What a shame that would have been. Laplace was an exceptional scientist. He not only came up with Bayes Rule by himself, but he also did more work than Bayes to contribute to humankind's understanding of probability, fought vigorously to separate religion and scientific inquiry, insisted on facts over belief, and was extremely productive in developing a foundation for statistics-- despite receiving so little reward. You will be treated to how, as a thank you from society, his life and reputation were ruined. Poor Laplace.

The author also provided a fairly good biography of other contributors to Bayes' Rule development and application throughout history. The rule itself was extremely unpopular. It's successes were hidden in wartime to protect war secrets. Those who used it were often bullied by the larger statistics community. And yet, the theory lived on, often under the radar, to continue helping researchers solve the hard problems. When the author provided a survey of how Bayes was used, I was familiar with the instances she highlighted but didn't realize Bayes was the method used to solve the problems at hand.

Since the author included, what I can only imagine, was every instance in which Bayes was employed, at times I felt like, "Yes, I have got it. Move on." I got a bit bored at times during the last few chapters. However, I think it would be unfair to criticize a book for including too much information about the focus subject:)

This was solid research, lots of it, that created a very thorough biography of the Rule/Theory itself. ...more

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Dec 25, 2011 Rafael Maia rated it it was ok

I wish I had liked this book more than I actually did. Most of the stories reported are very interesting and entertaining, reflecting how academics have been fiercely debating conceptual aspects of Bayes theorem, as well as the bayesian-frequentist feud, while at the same time it was being successfully applied in many crucial issues such as finding stray atomic weapons and linking smoking to lung cancer.

However, I did not find this book well-written at all. It's just not an exciting read - and i ...more

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Jun 08, 2013 Mike rated it it was amazing

Excellent and very readable book about the history of Bayes' theorem. I never realized that Bayesian statistics, one of the cornerstones of modern data science, had such a turbulent history--so turbulent that, during the cold war, being called a "bayesian" was tantamount to being called a Communist.

If you're at all interested in the history of mathematics, this is a surprisingly exciting story. I expected a rather dull and academic history; that is NOT what this book is. ...more

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Aug 14, 2011 Dennis Boccippio rated it really liked it

Shelves: math, 20th-century

It probably takes a special sort of person to dive into an entire book about one statistical theory, but for those so-motivated, this one pays off.

The pro's: The author has done a phenomenal job at capturing and richly detailing the very "large" personalities that have championed (or condemned) the use of Bayes' Rule through the centuries, amidst a little-known and long-simmering war that has persisted between statistical Bayesians and frequentists since the concept was first brought forward. T ...more

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Apr 19, 2014 Ms.pegasus rated it liked it · review of another edition

Recommends it for: anyone who has read the Nate Silver book SIGNAL AND THE NOISE

Recommended to Ms.pegasus by: citation if Nathan Silver's book

Shelves: history, nonfiction

As the subtitle proclaims, this book chronicles the history of science It also demonstrates how a simple formula evolved into a sophisticated application that required the invention of high speed computers to exploit its potential for prediction. It complements the information in Nate Silver's book, THE SIGNAL AND THE NOISE.

McGrayne introduces the reader to Bayes's Theorem with the proposal that given the unknown position of a billiard ball, its probable position can be narrowed by collecting da As the subtitle proclaims, this book chronicles the history of science It also demonstrates how a simple formula evolved into a sophisticated application that required the invention of high speed computers to exploit its potential for prediction. It complements the information in Nate Silver's book, THE SIGNAL AND THE NOISE.

McGrayne introduces the reader to Bayes's Theorem with the proposal that given the unknown position of a billiard ball, its probable position can be narrowed by collecting data about its spatial relation (right or left) to a succession of balls rolled randomly across the table. The technique is similar to the narrowing process that comes about during the game of “20 Questions.”

McGrayne then explains the concept of inverse probability: “We modify our opinions with objective information: Initial Beliefs … + Recent Objective Data... = A New and Improved Belief.” The initial belief is termed the prior probability and the revised belief is called the posterior probability. The idea was originated by Bayes, but was refined by Pierre-Simon Laplace, a French astronomer and mathematician. McGrayne contrasts the approaches of the two men as follows: “[Bayes] wanted to know the range of probabilities that something will happen in light of previous experience. Laplace wanted more: as a working scientist, he wanted to know the probability that certain measurements and numerical values associated with a phenomenon were realistic.” Her summary of Laplace's formulation is as follows: “...P(C|E), the probability of a hypotheses (given information), equals Pprior(C), our initial estimate of its probability, times P(E|C), the probability of each new piece of information (under the hypothesis), divided by the sum of the probabilities of the data in all possible hypotheses." She makes the case that Laplace had discovered the formulation by 1781.

The history of science is directed by many non-scientific incidents. The theorem fell out of favor in scientific circles, replaced by frequency-based probability methods. The focus of inquiry shifted to sampling methodology. As a result, we are all familiar with analysis based on the bell-shaped curve. How Bayes's Theorem stayed alive consumes the remainder of McGrayne's story. Much of this shift was due to the violently anti-Bayesian position of Ronald Fisher, a prominent British geneticist and statistician.

In the 1920's and '30's, the idea survived in the fields of financial economics, paternity law, biostatistics, and geology. Why? Because it provided practical data that could be used as a basis for action. During World War II the theorem received another boost. It was instrumental in cracking the German Enigma code. The effort was led by Alan Turing, whose interests spanned applied mathematics, machine language, codes and logic. He was a man of unconventional interests, a non-linguist, and a non-statistician. Above all, Turing was attracted to the Enigma problem because it was a challenge. No one else wanted to tackle the problem, and he enjoyed working alone. Meanwhile, Bayes's theorem was being applied in America by Claude Shannon at Bell Labs.

One problem for the resuscitation of Bayes's theorem was that all of this wartime work was classified. Post-war practice was kept alive in schools of business and actuary science. Academic mathematicians and statisticians ignored it.

To me, the most exciting post-war application was Albert Madansky's report on the probability of an accidental H-bomb detonation. Since there had never been an accidental detonation, frequency theory was of no help. Madansky's calculations included the fact that between 1950 and 1958 there had been more than 16 nuclear weapon related incidents – accidental drops, plane crashes, and handling errors of unarmed weapons. He factored in the proposed increase in SAC bombers and ICBM's, as well as the amount of handling that would be required. Even the air force calculated that 5 major plane accidents per 100,000 flying hours was a reasonable assumption. Madansky concluded that the expanded SAC proposal would make 19 “conspicuous” weapons accidents per year a high probability. The report resulted in significant changes in nuclear weapons handling procedures.

The early chapters of the book felt slow. They are primarily of interest to the historian seeking to verify the contributions to the theory by specific mathematicians. However, McGrayne does a convincing job of stressing the importance of Bayes's Theorem without going into the mathematical details. She also reveals interesting information about how academic rivalries, military secrecy, politics, and inter-disciplinary studies influence scientific progress. The latter is perhaps the most significant lesson this book offers to the general reader. Her many detailed historic examples make a compelling case for the importance of Bayes's Theorem in scientific analysis. ...more

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May 28, 2011 Converse rated it it was ok

Shelves: history, non-fiction, mathematics, statistics

Bayes' Rule is a mathematical formula that allows one to calculate a conditional probability (such as the probability that a woman has breast cancer given that she has a postive mammogram). It has many useful attributes, such as allowing one to updates ones estimates of a probability as you obtain new information, and can be adapted to deal with such basically non-numerical forms of information as expert opinion. One can also use it to estimate the probability of events that have not happened, such as a space shuttle blowing up in mid-air before the Challenger disaster.
Bayes rule has also been a subject of considerable controvery among academic statisticians throughout most of the twentieth century, with the controvery dying down since roughly the 1990s. This controvery, aside from showing the ability of academics to be touchy over what to the rest of the world must seem like minor matters, is rooted in a difference of opinion over the intellectual foundations of statistics. The frequentist school, as exemplified by R. A. Fisher, believed that probability is simply the relative frequency (for example, how many heads you get from a long series of coin tosses). The idea that one could come up with a probability about something that had not happened was anathema to frequentists. Also, they objected to the typical starting point for a Bayesian analysis, the assumption that all possible hypotheses were equally likely. The Bayesians, generally a minority view in academic circles, disapproved of the general frequentist approach of rejecting null hypotheses, as this approach actually involves extreme events that didn't actually appear in the data.

Bayes' Rule was kept alive in non-academic circles, and in academic disciplines outside of statistics. In particular insurance actuaries, and most especially the military, found Bayes' rule very useful. Bayes' rule is apparently especially helpful in breaking codes. Given the secrecy of such endeavors, the degree of military research in statistics is hard to know. The development of powerful computers also made Bayesian analyeses more generally practical from the 1980s onward.

The book is less a discussion of statistical issues than a history of statistics, starting with the Reverend Thomas Bayes himself in the 1700s. Most of the text is about 20th century events. At the end is a description of current uses of Bayes' rule. The reason I gave it "two stars" is that its not obvious to me that most readers will be able to follow the more technical aspects, such as references to Bayesian filters and such despite the glossary near the end. I think the historical approach results in less description and discussion of the statistical issues, and presumably the point of the book is to illuminate such matters. The historical approach may be interesting (I found much interesting material) but I would assume that people who pick up a book on this topic would mainly be interested in understanding statistics, rather than the doings of statisticians.

...more

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Jul 22, 2013 Herve rated it really liked it

It is the third book I read about statistics in a short while and it is probably the strangest. After my dear Taleb and his The Black Swan, after the more classical "Naked Statistics: Stripping the Dread from the Data", here is the history of the Bayesian statistics. If you do not know about Bayes, let me just add that I like the beautiful and symmetric formula: [According to wikipedia] For proposition A and evidence B, P(A|B) P(B) = P(B|A) P(A) with P(A), the prior, is the initial degree of bel It is the third book I read about statistics in a short while and it is probably the strangest. After my dear Taleb and his The Black Swan, after the more classical "Naked Statistics: Stripping the Dread from the Data", here is the history of the Bayesian statistics. If you do not know about Bayes, let me just add that I like the beautiful and symmetric formula: [According to wikipedia] For proposition A and evidence B, P(A|B) P(B) = P(B|A) P(A) with P(A), the prior, is the initial degree of belief in A. P(A|B), the posterior, is the degree of belief having accounted for B. The quotient P(B|A)/P(B) represents the support B provides for A. Another way of explaining it mathematically is Bayes' theorem gives the relationship between the probabilities of A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A).

I was never really comfortable with its applications. I was probably wrong again, given all what I learnt after reading Sharon Bertsch McGrayne's rich book. But I also understood why I was never comfortable: for three centuries, there's been a quasi-religious war between Bayesians and Frequentists on how to use probabilities. Are these linked to big, frequent numbers only or can they be applied for rare events? What is the probability of a rare event which may never occur or maybe just once? [Let me give you a personal example: I am interested in serial entrepreneurship, and did and still do tons of statistics on Stanford-related companies. I have more than 5'000 entrepreneurs, and more than 1'000 are serial. I have results showing that serial entrepeneurs are not on average better than one-time, using frequency and classical methods. But now I should think about using: P(Success|Serial) = P(Serial|Sucess) P(Success) / P(Serial) I am not sure what will come out, but I should try!].

If you want a good summary of the book, read the review by Andrew I. Daleby (pdf). McGrayne illustrates the "recent" history of statistics and probabilities through famous (Laplace) and less famous (Bayes) scientists, through famous (the Enigma machine and Alan Turing) and less famous (lost nuclear bombs) stories and it is a fascinating book. I am not convinced it is great at explaining the science, but the story telling is great. Indeed, it may not be about science at all. But about belief as is mentioned in the book: Swinburne inserted personal opinions into both the prior hunch and the supposedly objective data of Bayes' theorem to conclude that God was more than 50% likely to exist; later Swinburne would figure the probability of Jesus' resurrection at "something like 97 percent" [Page 177]. It obviously reminded me of Einstein's famous quote: "God does not play dice with the universe." This is not directly related but for the second time in my life, I was reading about links between science, probability and religion. ...more

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Jul 03, 2012 AJ Armstrong rated it really liked it

First, a cachet: unless you are already interested in one or more of Statistics, Decision Theory, Machine Learning, or the history and philosophy of Science and Mathematics, you are probably not a member of this book's audience. However, if you are, you will find a meticulously researched, erudite, and detailed survey of the history of statistics and decision theory. Undergraduate level familiarity with statistics and a generalist understanding of Bayes' rule would be very helpful but not critic First, a cachet: unless you are already interested in one or more of Statistics, Decision Theory, Machine Learning, or the history and philosophy of Science and Mathematics, you are probably not a member of this book's audience. However, if you are, you will find a meticulously researched, erudite, and detailed survey of the history of statistics and decision theory. Undergraduate level familiarity with statistics and a generalist understanding of Bayes' rule would be very helpful but not critical to enjoying the book and understanding the majority of its content (or at least its context in the narrative). The book's thematic focus is, obviously, Bayes' rule, but it touches on a whole panoply of ways in which science and mathematics have evolved into tools for everyday decision-making---including many of the roots of the modern world. Of particular interest is the tension between theory and practice, and how the Rule found its niche amongst those just trying to get work done, even while it was being ignored or rejected by pure theoreticians. A worthy read for anyone interested in these areas.

My only complaints are ones of emphasis, and might be more a matter of taste than anything else: I wish the author had been clearer about how what "Bayes' Rule" means has evolved and the fact that people who objected to it in the 19th century and those that objected to it in the middle part of the 20th were not necessarily objecting to the same thing. She also could have been clearer that what is "Baysian" has (due to its current fashionability) has broadened to the point that Bayes and LaPlace wouldn't recognize it, and that many so-called "Bayesian" techniques are strongly influenced by things that Frequentists would have had no problems with. Objecting to arbitrary priors isn't the same thing as objecting to many of the things that are now called Bayesian techniques. Finally, I wish she had been a little clearer that Bayes' value wasn't strongly evident until the ubiquity of cheap computational resources and the familiarity with the types of problems that large, complex systems generate became widespread in the theoretical community. Both of these trends had to wait until the later part of the 20th century, and so, frankly, did widespread acceptance of probabilistic reasoning under uncertainty. ...more

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Feb 09, 2012 Darrenglass rated it really liked it

A friend recently pointed out that the term 'Bayesian' is now entering the common parlance such that the NY Times can use it in an article without explanation. This would come as a huge surprise and disappointment to many statisticians from the early part of the 20th century, when Bayesian was a bad word and the theory was largely refuted. Why would a statistical theory be so upsetting, you might ask...well, McGrayne's book explains why, and gives the history of the theory over time and how it m ...more

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Sep 07, 2019 Adam rated it really liked it

Shelves: unwhiteman, qmss

Maybe I should stop rating books. I give this a somewhat tepid 4 stars. I enjoyed parts 1, 2, and 5, but found the story to drag at times in parts 3 and 4 (exceptions for the sections on smoking deaths and searching for nuclear weapons). I think that the Signal and the Noise does a better job of showing and actually explaining Bayes theorem, but it's also a much longer book and has room to do that. ...more

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Mar 12, 2016 Kristin Lieber rated it it was amazing

Impressive research, an enjoyable read about the history of Bayesian statistics. However, lacks a good description about the basic question – what is Bayesian statistics. The book would benefit from a first chapter with a couple engaging examples of how Bayes works. Must be able to last through the first couple dry chapters.

Bayes helps real-life practitioners assess evidence, combine every possible form of information, and cope with the gaps and uncertainties in their knowledge. Some of Bayes’ Impressive research, an enjoyable read about the history of Bayesian statistics. However, lacks a good description about the basic question – what is Bayesian statistics. The book would benefit from a first chapter with a couple engaging examples of how Bayes works. Must be able to last through the first couple dry chapters.

Bayes helps real-life practitioners assess evidence, combine every possible form of information, and cope with the gaps and uncertainties in their knowledge. Some of Bayes’ powers is that it allows a researcher to stop running an experiment when data was sufficient, monitor interim results, examine effects on subgroups or follow leads from the data with further unplanned analyses. It helps scientists with scanty data and computing probabilities of highly unlikely events.

Frequentists methods work for repetitive, standardized phenomena, while Bayes incorporates a variety of sources of information. Decisionmakers often want to look at more than one alternative not merely accept or reject a hypothesis. It is useful for decisionmaking, helpful because it allows comparing multiple models. Bayes then expresses answers in terms of probabilities.

Bayes vulnerability is that its magical powers depend on the validity of its probabilistic inputs. There are the computational difficulty of Bayes – as the number of unknowns rise, integration problems become difficult. Recent advances in the combination of Bayes and MCMC (Markov chain Monte Carlo) has been called arguably the most powerful mechanism ever created for processing data and knowledge. I got the sense that this replaces integration with approximation techniques through series.

The book has a favorite quote about statistics…. "no one has ever claimed that statistics was the queen of the sciences..The best alternative that has occurred to me is bedfellow. Statistics – bedfellow of the sciences.” Ends with conclusion that there has been a truce between frequentists and Bayesian and most modern Bayesians accept that the frequentist approach is still effective for most statistical problems.
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Apr 05, 2012 Andy rated it it was ok

There is some very important information here but it is buried under a giant pile of whocares?.

By giving us the life of Bayes, the childhood of Laplace , ... , I think the author is trying to force the book to have a narrative, but I doubt that many people buying books about mathematical theories are interested in the minor details of the mathematicians' lives. This type of writing would be bad enough if the importance of Bayesian analysis were clearly explained, but it isn't. For instance, in ...more

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Oct 28, 2017 Rebecca rated it did not like it

Shelves: could-not-finish

I initially thought this book would be more scientific and talk about how Bayes Theorem helped solve various problems throughout history. However, this was more of a history book, which is not something that I have ever read as history just isn't something I've ever been interested in. Anyway, I understand that the book was on the side of Bayes' Theorem but I felt as though the author made those who study traditional statistics (not Bayesian stats) were the bad guys and she spent a lot of time, ...more

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Mar 20, 2019 Rebekka Lisøy rated it liked it

Shelves: audio-read

This book was interesting, but also a bit odd. As I see it, if someone thinks a book on the history of Bayes’ theorem sounds interesting, then this person is most likely already familiar with Bayes. Yet, it seems like this book was written for an audience with little or no knowledge of Bayes, which means that a lot of the “technical” details were left out. You are presented with interesting stories about how someone used Bayes to, for example, figure out where a bomb was accidentally dropped in ...more

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Jan 06, 2012 Dan rated it it was ok

Shelves: history-of-science

Covers the history of Bayes' rule but there's little on actual mathematical application. The book was heavy on mathematician drama and light on data-driven aha! moments. If you are interested mainly in History of Mathematics, raise this review to 3.5 stars. But the book's subtitle is misleading: rather than "_how_ Bayes' rule cracked the Enigma code..." it should read "_that_ Bayes' rule cracked the Enigma code..." since there's little "how" to be had. An interesting piece of history, but ultima ...more

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Sep 02, 2013 Rajesh Israni rated it really liked it

My following review on "The Theory That would Not Die" is not just a review of the book, but also a detailed account of the actual Bayesian theory and its numerous benefits that unfortunately still remain hidden from general public. I hope that by sharing the importance of this great piece of theory it might kindle your interest to learn more and read this delightful book by Sharon Bertsch McGrayne. To understand the importance and the concept of Bayes Theorem it’s important to establish its nee ...more

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Mar 27, 2021 Roy rated it really liked it

Shelves: how-the-world-works, fcpl, science-popular, own-audio, history, gen-non-fiction, government-successes, connection-to-my-life, decision-making, math-prob-stat

Really an interesting, unusual book that combines history, math, and decision theory into a discussion about several of the most useful ideas in probability theory. Although a bit preachy at times, and clearly of the perspective that frequentists slowed down several fields of science, I think it tells the tale of the evolution of probability theory very well -- ironically the whole field, not just the Bayesian aspects of probability.

I think McGrayne does a really good job of putting into context Really an interesting, unusual book that combines history, math, and decision theory into a discussion about several of the most useful ideas in probability theory. Although a bit preachy at times, and clearly of the perspective that frequentists slowed down several fields of science, I think it tells the tale of the evolution of probability theory very well -- ironically the whole field, not just the Bayesian aspects of probability.

I think McGrayne does a really good job of putting into context the development of probability as a branch of mathematics, with the usual mix of progress being driven by practical problems that need solving, theoretical insights, persistent work, the availability of new tools (especially in this case, computers), and, inevitably, the personalities of the people involved. She highlights the names I knew, and gives attention to some figures that were obscure to me.

Particularly intriguing to me is her speculation that the classified nature of much work on applying Bayes theorem in the twentieth century -- because it proved so useful in cryptography and military operations research -- sustained badly-argued philosophical debates within mathematics and science, and did so specifically because the development of practical Bayesian solutions and improvement of technique could not be shared with the broader scientific community. She makes an intriguing case that this secrecy was the reason the world seemed for a time, in the middle of the last century, to be divided into warring religions of Bayesians and Frequentists.

As a pragmatist myself, I rarely believe that philosophical debates affect the proper role of mathematics. Like Bacon, I believe it's only knowledge if it is useful, and, obviously, both the frequentists and the Bayesians produced tools that are useful. I will admit, though, that I didn't know how many of the tools of decision theory and hypothesis testing that I regularly employ, and even teach, came out of this debate, nor how my approach to work and teaching would likely have been labeled Bayesian if I were in the last century. To me, Bayes is the only practical tool for many problems ... but, as I like to point out to students, in many situations you can get the same answer from either approach.

The book isn't quite a five-star book for me because of two things. First, I really think that the book overdoes a sense of heroes and villains in this story: these mathematicians, theoretical and applied, were largely trying to establish a rigorous basis for solving problems, and I think their differences and passion, on both sides, is largely to be admired; and I think that the fact that they went too far in ostracizing their rivals is just a sign of human failings more than villainy. Second, I wish there had been more math and references, particularly in the last chapters where she begins to show the triumphant application of Bayesian analysis in an age of computing power. I found that she was describing the current synthesis of probability and decision analysis that I came of age in, and I would have liked to seen more detail there. Whole chapters on LaPlace may be justified, but cramming all the great inventions of the 1980s into a few paragraphs seems unbalanced to me. ...more

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Oct 31, 2019 Prasanna rated it liked it

I like mathematical history books and this book has a lot of behind the scenes stories of how Bayes Rule came to be what it is right now and the statistical community's aversion to using it. What I found really fascinating was how instrumental Laplace was in the development of Bayesian theory, and how Turing applied it during the war. I found the usages mentioned later for finding the nuclear bomb to be a bit of a stretch at the time. Although it has eventually found its use. The book makes me t I like mathematical history books and this book has a lot of behind the scenes stories of how Bayes Rule came to be what it is right now and the statistical community's aversion to using it. What I found really fascinating was how instrumental Laplace was in the development of Bayesian theory, and how Turing applied it during the war. I found the usages mentioned later for finding the nuclear bomb to be a bit of a stretch at the time. Although it has eventually found its use. The book makes me think that since a lot of applications didn't call themselves bayesian and came to the solution from different angles, just painting them retroactively as bayesian isn't a fair assessment.
Broadly speaking this book treats Bayesian methods and inference as the process of taking assumptions of priors and updating beliefs. This was deemed to be too subjective in Rev. Bayes' era by the broad scientific community and I was surprised to find that Bayes' interest comes from David Hume's skeptical essay on the cause and effect relationships, i.e., God being the first mover. This was further championed by Richard Price. Further practical work done by Laplace.
I found Laplace's story and his intersection with french politics to be fascinating, apparently he had launched Napoleon on his military career by giving him a passing grade in military school.
The second world war, and Turing's usage of Bayesian methods in detecting russian subs and protecting the allies ships was as much inspiring as heartbreaking. Despite doing a lot of work that should've garnered him recognition, all the work was classified and he didn't have the status that could've protected him from persecution. The author suggests that had Turing been knighted after the war for his efforts, it would've given him a lot more protection and ability to work on what he wanted to.
A lot of internal strifes within statistical community wasn't that fascinating to me. Partly because it was mostly people outside of the community that saw the practical usages and were able to utilize Bayesian methods to make them popular. The book would likely be incomplete without that and it provides intrigue. But anyone who has worked in scientific community knows that these factions are all too common.
Overall this is a solid book and highly recommend it as a filler for understanding the historical underpinnings for the rise of Bayesian theory. ...more

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Apr 05, 2021 briz rated it liked it

My reading speed asymptotically approached zero as this book progressed. Alas!

A history of science book, this covers the history of Bayesian statistics - from its origin in 18th century England via Thomas Bayes, to its second origin in 18th century France with Laplace, to its waxing and waning in popularity throughout the 20th century, and eventual redemption thanks to increased computational speed/processing power. A lot of the 20th century stuff seemed to be directly taken from interviews, so My reading speed asymptotically approached zero as this book progressed. Alas!

A history of science book, this covers the history of Bayesian statistics - from its origin in 18th century England via Thomas Bayes, to its second origin in 18th century France with Laplace, to its waxing and waning in popularity throughout the 20th century, and eventual redemption thanks to increased computational speed/processing power. A lot of the 20th century stuff seemed to be directly taken from interviews, so the book has an oral history quality to it. And it's certainly written in a lively, impassioned way.

But! It's also frustratingly vague of what "Bayesianism" actually IS (we do see Bayes' Rule once, early on in the Laplace chapter, and we have a lot of discussions of how people get upset about priors). But for a science book, I feel like it fails to convey the core insight of what makes Bayesian stats interesting. We talk a lot ABOUT Bayesian stats, but unlike e.g. Michio Kaku re: fancy physics (and maybe physicists will balk), or Emily Oster (or Esther Duflo and Abhijit Banerjee) and economics, or Michael Lewis and economics/anything, this book doesn't really inform the reader on the core idea. And I get it! It's hard. And I can't even pinpoint specifically HOW McGrayne doesn't get it right... Like, she definitely does spend a lot of time discussing priors, uncertainty, beliefs/probabilities, and frequentist's contrasting ideas of multiple samples (and how who has time/money to do _that_?!). But it almost feels like she spends a lot of time discussing these topics without ever first defining them in great depth.

Similarly, another thing which started to really grate on me was the long, comma-separated lists of applications of Bayesian stats (lists and lists and lists), as well as McGrayne's tendency to introduce numerous people in the same way: Robert ("Bob") Smith, who received a PhD from Ivy League University, blah blah. Do I need to know he went by Bob? Also, these appeals to authority (PhD from Ivy League!) definitely worked on me in the beginning ("wow, Bayes is so mathy, these people are so well-qualified"), but then I started to be like, "wait, why do I need to know Bob goes by Bob and went to Yale if I'm never going to hear from him again?"

I was also was a little miffed by the relatively cursory mention of Bayes's history in economics ("oh yeah, Tversky and Kahneman won the Nobel for showing people aren't super rational"), while we spent - relatively - soooooo much time with military applications. And I mean, I like the Navy! I like to read about naval things! But I also became enamored with Bayes, like a lot of people in my classes, when going through the econ journey of game theory, risk and uncertainty, decision making under risk and uncertainty, and finally behavioral economics. This is a wonderful journey! A very interesting realm of study! So yeah, I was miffed that in a big book about Bayes, we spent so much time at Harvard Business School and the Navy, and so little time with, indeed, Kahneman and Tversky. ...more

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Jan 30, 2019 Ed Terrell rated it it was amazing

Shelves: 2019

Bayes (including MCMC) had been called “arguably the most powerful mechanism ever created for processing data and knowledge“

“The Theory That Would Not Die” is well written, informative and an engaging read. From its roots in the "principle of inverse probability”, Bayes rule and Laplacean probability now have numerous newer references and more nuanced meanings. Bayesian probabilities, Bayesian statistical inference (or more simply Bayesian inference), probability based statistics, probability of ...more

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Feb 14, 2021 Song rated it it was amazing

Shelves: history, science, mathematics

This is a science history book about the Bayes Theorem, full of interesting details and insights about how human beings applied this equation to almost all areas of human lives.

In the essence, the topic of the book is about a mathematical theory. And usually, any theme related to math will be dry, hard to understand, and average readers will shun away from it. But this book is exceptional. On the contrary, with the extensive research done by the author, the science history of Bayes Theorem is tu ...more

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Dec 10, 2021 F Avery rated it liked it

Disclaimer: I have graduate degrees in mathematics and electrical engineering, in which I studied and used Bayes rule and other tools of statical inference, so perhaps I don’t qualify as the typical reader of a book of this type.
I vacillated between a rating of 3 or 4 but have decided to go with the former. On the one hand, the author gives interesting historical background on Bayes rule that I was not aware of, including Bayes’ own formulation, the documentation by Price, and LaPlace’s analysis ...more

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Dec 05, 2021 Vince Snow rated it liked it

I really liked the book and it was a quick and fun read. I knew only a bit about Bayesian analysis prior to the book and I didn’t know what exactly bayes rule was. I found some of the anecdotes in the book very fascinating including the part about Turing during ww2 and when they searched for submarines on the bottom of the ocean. Where I felt like the book was lacking was that maybe I just don’t know much about frequentists, but it just railed against them for 200 pages. It’s very possible that ...more

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Feb 05, 2022 John Senner rated it really liked it

Bayes Theorem is essentially a mathematical statement that an opinion of the probability of event can be changed by new facts. That seemingly mundane conclusion lay in obscurity and then was revived to great controversy between the "frequentists" and the "Bayesians." Alas I was born too soon. My statistical education was pure frequentist. I just started with WORDLE which is purely Baysian. You take a guess. The dark letters are a fact that increases the probability that a grey letter will be cor ...more

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May 21, 2020 Renee rated it it was amazing

Slow but wonderful book. I started this on an airplane pre-covid, so that tells you how long it took me to read. I could only do small pieces at a time. But who knew you could make a history of statistics fascinating? The author truly does phenomenal research and organization and storytelling. I am so impressed. I learned a ton of random facts and more detail around people I knew so little about.

I do agree with other reviewers that the appendix material would have helped immensely up front inste ...more

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May 11, 2021 Alice rated it really liked it

I have been obsessing over this book the entire week. Re-reading and Googling, questioning and applying. I (as a microeconomic theorist) found it inspiring, not only because I use the theorem every day but also for the story on the development of ideas and how they spread through the scientific community. I would have dearly appreciated at least an appendix with the technical arguments in question.

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Jul 12, 2018 Nehal Singh rated it really liked it

A truly detailed and fascinating history of Bayes theorem, a little exhausting in the later half because of the sheer amount of information in the book (it is a history book after all) but a small suggestion that worked for me - breeze over the historical details (seasoned readers would know what I'm talking about) and don't try to retain them - but pause and think over the interesting bits (like Bayes' first experiment) and make sure you understand the essential concept of the theorem in mathem ...more

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About Sharon Bertsch McGrayne

Sharon Bertsch McGrayne

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Sharon Bertsch McGrayne is the author of highly-praised books about scientific discoveries and the scientists who make them. She is interested in exploring the cutting-edge connection between social issues and scientific progress – and in making the science clear and interesting to non-specialists.

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“The combination of Bayes and Markov Chain Monte Carlo has been called "arguably the most powerful mechanism ever created for processing data and knowledge."
Almost instantaneously MCMC and Gibbs sampling changed statisticians' entire method of attacking problems. In the words of Thomas Kuhn, it was a paradigm shift. MCMC solved real problems, used computer algorithms instead of theorems, and led statisticians and scientists into a worked where "exact" meant "simulated" and repetitive computer operations replaced mathematical equations. It was a quantum leap in statistics.” — 2 likes

“Yet Laplace had built his probability theory on intuition. As far as he was concerned, "essentially, the theory of probability is nothing but good common sense reduced to mathematics. It provides an exact appreciation of what sound minds feel with a kind of instinct, frequently without being able to account for it.” — 1 likes

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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

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