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

Sep 03, 2012 rmn rated it 2 of 5 stars

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...more 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.(less)

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Apr 12, 2012 Marks54 rated it 3 of 5 stars

The was an interesting popular history of the progress of "Bayes' Rule" from its inception to the present. The rule is about calculating probabilities based on base rates that are updated with subsequent information. The overall history quickly becomes a history of frequency versus Baysian approaches and the tribalism that goes with academic infighting. That is interesting up to a point but seems a bit overdone. Another narrative in the book is how the conditional approaches become more popular...more

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Dec 25, 2011 Rafael Maia rated it 2 of 5 stars

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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May 28, 2011 Converse rated it 2 of 5 stars

Shelves: statistics, non-fiction, mathematics, history

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,

...more

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.

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Mar 28, 2013 Alex Apffel added it

Shelves: science

In 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 Bersch McGrayne takes what might be an otherwise stereotypically dull subject (statistics) and spins a fascinating story across 250 years that touches on Fanatacism, Scientific Breakthroughs, Codebreaking, Academic Feuds and the general idea of how strongly people cling to their beliefs of the "right" way to do things.

Here are...more In 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 Bersch McGrayne takes what might be an otherwise stereotypically dull subject (statistics) and spins a fascinating story across 250 years that touches on Fanatacism, Scientific Breakthroughs, Codebreaking, Academic Feuds and the general idea of how strongly people cling to their beliefs of the "right" way to do things.

Here are four interesting tidbits that I found fascinating from this book.
1. Somewhere around 1755, Thomas Bayes, a presbyterian, non-conformist minister in Tunbridge Wells, Kent developed a method for what are known as "inverse probability" problems, in other words, given that certain conditions exist, what is the probability that a specific event will occur. Although Bayes was a member of the Royal Society for other work concerning mathematics, this work for which he is known, was not published until after his death when it was communicated to the Royal Society by his friend, Richard Price. What is amazing, is that in its original format, there were no real interesting problems and the use of "Bayes' Theorem" required intensive iterative calculations that were impractical until either shortcuts or electronic computers were developed.
2. Although we call it "Bayesian", much of filling in the details was initially done by Price, but more importantly by Pierre Simon Laplace who in 1814 published an essay on a mathematical system for inductive reasoning based on probability. This really put the whole concept on a firm footing. Laplace also worked out mathmatical techniques based on transforms, expansions and logarithms that made some of the calculations tractable. Nonetheless, nobody calls it Laplacian Probability.
3. During World War II, much of the code breaking done by Alan Turing at Bletchly Park was based on Bayesian Inference, which Turing seems to have rediscovered independently. This was extraordinarily successful. There's a great story here. However, what was astonishing was that all of this information (including Turing's involvement) was classified as Ultra Top-Secret until the 1970s because of the implications of the cryptography during the cold war. Not only did this mean that the Bayesian Techniques and their successes were unknown, but Turing's involvement and contribution was also unrecognized during his lifetime, with tragic consequences.
4. Finally, the constant thread and most fascinating part of this story is that for almost 250 years, there has been a bitter dogmatic war between frequentist statisticians and and proabablistic statisticians. There were centers of Frequentist Faith like Berkeley that decried the probalistic approach as nonsense (or worse). Running dialogs in the scientific literature had noted staticians call each names...
The technique is now widely accepted for a range of applications. The real turning point came when people applied the bayesian technique to solve problems instead of theorized about the value of the approach !(less)

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Aug 21, 2012 Gloria rated it 3 of 5 stars

This is a history of the progress of Bayes' theorem from the early 1700s up to the present. There is essentially no mathematics in the book; it is simply a historical account of the development of Bayes' theorem, with details of the major players in this development and description of how the concept was used in various scenarios in 'the real world' (an aside: how I hate the phrase 'in the real world' , so silly. As if mathematics isn't real. Oh come come). However, having said that, this is a v...more

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Jul 12, 2012 AJ Armstrong rated it 4 of 5 stars

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...more 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.(less)

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Jun 18, 2013 Gwern rated it 4 of 5 stars

Light history of Bayesian statistics & related topics. I enjoyed the book a lot; McGrayne has a good eye for the amusing details, and she conveys at least some of the intuition (although some graphs or examples would have helped the reader - I liked the flipping coin illustrations in Dasivia 2006 _Bayesian Data Analysis_). It's also remarkably synoptic: I was repeatedly surprised by names popping up in the chronology, like BUGS, Bretthorst, Fisher's smoking papers, Diaconis, the actuarial us...more

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Feb 09, 2012 Darrenglass rated it 4 of 5 stars

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 02, 2011 Jason rated it 3 of 5 stars

Shelves: nonfiction, science, mathematics

Sharon McGrayne is a very good and engaging writer. She has an interesting story to tell about the last 250 years of Bayesian thinking, how the theory has developed, and its many applications including how to price insurance, how to aim artillery, how to break the Enigma code, who wrote The Federalist Papers, how to find Russian nuclear subs, how to estimate the probability of a shuttle disaster, when to do various cancer screenings, whether cigarette smoking is harmful, etc. She also has a grea...more

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Mar 18, 2013 Terry rated it 3 of 5 stars

Shelves: 2013, history, math, non-fiction, audiobook

The Theory That Would Not Die is a history of Bayes' Theorem and the struggle Bayesianism has been in with frequentism for the two centuries. I found the book enjoyable but there were two shortcomings:

1) The depth to which a particular example was taken was highly variable. Some things were merely mentioned while others were reviewed in great detail. The best chapters explaining the applications of Bayes' Theorem occurred 2/3rds of the way through the book, well after the explanation would have...more

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Apr 05, 2012 Steve rated it 3 of 5 stars

Shelves: non-fiction, science

I came to this book hoping to understand what the heck scientists mean when they say they use a Bayesian approach or Bayesian statistical analysis, but without having to decipher too many formulas or greek letters. However, the book may have erred too much on the side of popular nonfiction; I'm surprised that after reading, I only have a slightly better understanding of Bayes than before.

But I can't exactly fault the author. I doubt there is much market for a popular explanation of Bayesian sta...more

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Dec 26, 2012 Ken rated it 4 of 5 stars

I liked this book a lot more than I thought I would, particularly given its ratings. This is a non-technical history of the use of Bayesian statistics. The book is so non-technical that no background in statistics is really required at all. The non-technical nature also comes at the cost of a lack of detail. The book only explains WHY Bayesian methods were so poorly thought of for years at a very high level, without enough detail to really understand the underlying issues. In addition, its descr...more

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Apr 05, 2012 Andy rated it 2 of 5 stars

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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Sep 30, 2012 Romann Weber rated it 3 of 5 stars

Interesting, dry, and disorganized ... often within the same page. McGrayne has produced a well-researched book on a very important topic. However, I believe she does the reader a disservice by shying away from some mathematical notation (and consequently, precision) in her definition of what Bayes's rule really is, especially since it is so easy to prove and would not scare off anyone likely to be reading this book.

The Bayesian controversy starts, of course, with the interpretation of "priors,"...more

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Jun 28, 2011 Jeff rated it 3 of 5 stars

The basic idea of Bayes' Rule is that you treat probability as a degree of belief (i.e. how much are you willing to bet on something) instead of a relative frequency (i.e. count the number of royal flushes out of all possible poker hands).

Bayes' Rule allows you to "learn" by updating your (prior) degree of belief of something (i.e. probability of finding a sunken ship in a certain part of the ocean) given new information (i.e. a captain's log) in order to obtain knowledge in a "posterior" belie...more The basic idea of Bayes' Rule is that you treat probability as a degree of belief (i.e. how much are you willing to bet on something) instead of a relative frequency (i.e. count the number of royal flushes out of all possible poker hands).

Bayes' Rule allows you to "learn" by updating your (prior) degree of belief of something (i.e. probability of finding a sunken ship in a certain part of the ocean) given new information (i.e. a captain's log) in order to obtain knowledge in a "posterior" belief. It's a bit "messier", but it tends to get good results with more data. This approach allows you to calculate probabilities for things you couldn't realistically count frequencies for (because they haven't happened before)

Bayes' Rule was often ridiculed before computational power made its tedious calculations possible. In addition, people didn't like the fact that you had to kickstart Bayes Rule with a "prior" that tended to be subjective (even if it's better than nothing).

The book highlights the story of the discovery of the rule and its ridicule for ~250 years until it came to dominate the world of today in lots of applications (i.e. used in Google's spellchecker, spam filters, etc)

Some interesting quotes/notes:

* "In a new kind of paradigm shift for a pragmatic world, the man who had called Bayes 'the crack cocaine of statistics... seductive, addictive and ultimately destructive' began recruiting Bayesians for Google."
* Although Bayes gets most of the credit, Laplace did most of the real work to get the rule in its modern form.
* There was a cool explanation of a Bayesian application of determining authorship of the "anonymous" Federalist papers using spam-like Bayes rule. Very interesting.
* The book describes the search for a sunken submarine (Scorpion) using Bayes' Rule relying on accounts from Lawrence (Larry) Stone. I originally learned about Bayes Rule when I worked as an intern with Larry, so it was cool to see things come full circle reading about the adventure in this book (wasn't expecting it!)
* "In 1996 Bill Gates, cofounder of Microsoft, made Bayes headline news by announcing that Microsoft's competitive advantage lay in its expertise in Bayesian networks."
* "According to Google's research director, Peter Norvig, 'There must have been a dozen of times when a project started with naive Bayes, just because it was easy to do and we expected to replace it with something more sophisticated later, but in the end the vast amount of data meant that a more complex technique was not needed."

I liked the book. I would have enjoyed it more with more technical details, but realize this wasn't likely given the wide intended audience.(less)

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Jan 06, 2012 Dan rated it 2 of 5 stars

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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Dec 29, 2012 Michael Quinn rated it 3 of 5 stars

Really just a series of very short biographies on major statisticians and probability theorists since Thomas Bayes. The stuff on Laplace is nice, and the stuff on Turing is very touching. Otherwise, that's about it.

On the whole, the book feels dumbed down. The formula itself only shows up twice in the entire book. While there are lots of stories of its application, more details on the mechanics would have been appreciated. Maybe this is an impossible wish, since the inclusion of any real amount...more

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Aug 27, 2011 Tom rated it 3 of 5 stars

This was a very interesting read. It seems like common sense that one would use prior experiences to help predict what might happen in an uncertain future situation, but apparently that was a pretty radical notion at one time. At times the self-importance of academia inserts itself into the story, as if anyone really cares if the guy 200 years ago or 150 years ago deserved to have the theory named after him, and the frequentist/Bayesian debate often seems really, really stupid. The examples of a...more

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Jan 06, 2012 Michael rated it 2 of 5 stars

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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Oct 03, 2011 Dennis Boccippio rated it 4 of 5 stars

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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Feb 18, 2012 David rated it 4 of 5 stars

Shelves: mathematics, history, technology

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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Sep 10, 2011 Carolyn rated it 3 of 5 stars

Shelves: essays, library-books, nonfiction, popular-science, history

A couple of hundred years after Bayes formulated his rule, it was almost universally scorned, despite the fact that it worked: most dramatically, Turing used it to decrypt the Nazi Enigma code machine. The vindication of Bayes was as dramatic and controversial in the world of mathematics as was the vindication of the theory of continental drift in the mid 20th century. Still, there was none of the discussion I wanted to see: how Bayes' rule debunks many of the articles of faith of the promoters...more

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Jun 08, 2013 Mike rated it 5 of 5 stars

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.

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Oct 14, 2012 Caroline rated it 5 of 5 stars · review of another edition Recommends it for: math nerds

Shelves: math, non-fiction

One of the most exciting books I've read in years. I'd can't recommend this book highly enough. It's completely approachable to the layperson, but so incredibly interesting. I was astounded at what Bayes' rule has been used for, and just have to learn more. I've loved seeing how it shows up a little bit in my probability and statistics textbook, but am planning to go buy one or several bayesian specific textbooks to learn more.

My only complaint is that I would have loved more and harder example...more

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Nov 03, 2012 Richard rated it 3 of 5 stars

The history of Bayes' rule is very interesting and so are some of the applications outlined in this book such as the location of the french airliner that had crashed in the south pacific.
Although i enjoyed reading the historical content of bayes' rule, i feel that the writer did not present the content in a "ingestible" way. i felt as though it was like reading through a school text book and felt more like a chore rather than leisure.

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Feb 08, 2013 Nigel Davies rated it 1 of 5 stars

I was deeply disappointed by this book. I badly wanted to like it, but I couldn't. I wanted to understand how Bayes theorem had solved the problems described on the cover, but a comprehensible explanation (with a little maths) was missing. Instead the author built up a, to my mind false, conflict between the Bayesians and the Frequentists. And she didn't even trouble to explain what the Frequentists were, when they were first invoked.

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Apr 06, 2012 JParsons1974 Parsons rated it 5 of 5 stars

Shelves: business

Even if you failed math in college this book is good. Basically it's a history one statistical theorem. Put simply by updating intial your belief about something with objective new information , you get a new and improved belief. So simple but so controvrsial. The book is not easy to read in fact I was Googling some of the ideas, persons, places mentioned to understand what was going on but in the end it was worth all the time spent.

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Jan 29, 2013 David rated it 4 of 5 stars

This is an excellent book if you need to build motivation to learn more about Bayesian methods. It gives you a good qualitative sense of what they're good for.
It's also completely devoid of any information about how they actually work, which is a bit disappointing. However if you're OK with learning that from other sources, and are just interested in an historical overview, it's fine and entertaining science journalism.

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Nov 08, 2011 Erik rated it 3 of 5 stars

A really interesting review of Bayesian statistics and the battle between Bayesians and frequentists ( the conventional type of statistics you probably learned about in school). While I found the book to be a little lite on describing actual Bayesian techniques, the book was enough to inspire to go pick up a more technical text so I can start using Bayesian techniques in my own life/work.

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