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

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,

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.