Å·±¦ÓéÀÖ

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.