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 [Hardcover]

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.

This is an excellent history of the development and application of Bayes' Theorem. Intended for the general reader with an interest in probability and the history of science, it is clearly written with a minimum of mathematics, and covers the ground efficiently.

It is particularly interesting for what it reveals of the way in which new ideas become part of intellectual discourse; in this case, by enduring a long period of suspicion and neglect before being rescued by the enthusiasm of practitioners rather than theorists. McGrayne offers many sidelights on the clandestine uses made of Bayes by the military and the intelligence community, which go some way to explaining why the power of these techniques was so long in receiving acknowledgement. The powerful personalities of the people involved receive extensive attention: no reader will come away from this book in ignorance of the degree to which accidents of institutional history and personal character condition the intellectual environment. Recommended.

This is half a book and the half is very good - it would be worth 5 stars. You learn about the fascinating people who deployed Bayesian inference, particularly the Enigma codebreakers; about the statisticians who thought it was a complete waste of time; about the quirks of history which made people so slow to recognize its value.

All very good. But this is a book about some mathematics, and there is very little maths! Bayes' rule gets an equation, but that's not actually Bayesian inference. The author keeps saying that sometimes frequentists and Bayesians get the same results, but no example. And sometimes very different results, but no example. Bayes himself seems to have proved it, but no details on the proof. Some other people seem to have proved it, but ditto. Bayesian calculations are said to be very difficult pre-computer and pre-MCMC, but no example so you can see why it's such a problem.

So: a little disappointing - but maybe it does provide the questions you can type into Google after this book has not provided the answers.