The Theory That Would Not Die: How Bayes’ Rule Cracked The Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant From Two Centuries Of Controversy, by Sharon Bertsch McGrayne

The intersection of probability, politics, and history is a strange place for a book to find itself. One of the chief elements of this book, and whether it is a good thing or a bad thing I am not exactly sure, is that Bayes’ rule has often rubbed people in mathematics the wrong way. If, at least at present, its place seems secure within the world of mathematics, this is only a very recent phenomenon, and even within my own lifetime (which is not really all that long, it must be admitted), Bayesian probability was considered a highly controversial and even illegitimate endeavor for a serious-minded statistician to be involved in. There is an essential divide in how the rule has been viewed over the past two hundred years or so. On the one hand, the rule is interesting and leads to highly worthwhile practical achievements. On the other hand, though, the rule has assumptions and implications that are unsettling to many and that lead the rule to have been viewed for long periods of time with a great deal of disfavor. Indeed, many of those who used Bayesian probability were either unaware of the fact, which is not too surprising given how obscure the rule was in mathematical education, or had to deliberately keep it private in order not to offend powerful academic interests and impede their own career progress.

What is it about this rule, and the way that it appears to give a secure and important place to subjective hunches that take advantage of prior knowledge that has made this rule so uncomfortable to many engaged in probability who have insisted on maintaining their focus on p-values and null hypotheses and the assumption of normal distributions and the like? What makes one set of assumptions properly scientific and the other subjectivist? As someone who comes from a background of practical probability rather than theoretical mathematics, I have always had a fondness for Bayes’ rule and a high degree of its practical sense, though I have seldom involved myself in the struggles that the rule has faced within the mathematical community. One can generally get a good sense that people often tend to woefully underestimate the chances that things will go differently than their preferred model, and in some cases (like the Challenger disaster), the results of a complacent belief that things will go alright without vigilance and awareness of how many things can go wrong are often tragic and deadly. Bayes’ rule provides a good understanding that learns as you gather more information, and if it was useful in previous generations without much computing power, it has become even more important in contemporary applications, which is perhaps what some people might not have thought but it has proven to be very intriguing, at least.

In terms of its contents, this book is a bit more than 250 pages divided into five parts and seventeen chapters. The author begins with a preface and note to readers and acknowledgements. This is followed by the first part of the book, containing three chapters about the Enlightenment and the Anti-Bayesian reaction (I), discussing the issue of causes up in the air (1), LaPlace’s importance (2), and the fact that from the start Bayes’ rule had many doubters and few defenders (3). The second part of the book then moves to the Second World War era (II), with chapters on the use of Bayes’ rule in war (4) and the premature burial of Bayes’ thinking once the war was one (5). Several more chapters are taken looking at the slow recovery of Bayes’ thinking in the period after World War II (III), with a discussion of Arthur Bailey (6), the way that Bayes’ thinking moved from a tool to theology (7), Jerome Cornfield (8), as well as early efforts at building a Bayesian community (9) that included staggering complexity (10). This is followed by several chapters that show how Bayes’ rule proved its worth in the age of rising computing power (IV), with chapters on its use in business decisions (11), the study of how to determine who wrote various Federalist papers (12), the importance of Bayes’ rule in the Cold War (13), Three Mile Island (14), and Navy searches (15). The last part of the book then discusses the victory of Bayes’ thinking (V), with an understanding of why Bayes’ rule works well (16), and the importance of Bayes’ thinking in translation (17). Two appendices then follow discussing Dr. Fisher’s casebook and an application of Bayes’ rule to mammograms and breast cancer rates, after which the book ends with notes, a glossary, bibliography, and index.