Kevin Spacey famously said that the greatest trick the Devil ever pulled was convincing the world he didn’t exist. When it comes The Search for Certainty, a new book on the philosophy of statistics by mathematician Krzysztof Burdzy, the greatest trick involved was getting a copy into the hands of Christian Robert, who trashed it on his blog and then passed it on to me.
The flavor of the book is given from this quotation from the back cover: “Similarly, the ‘Bayesian statistics’ shares nothing in common with the ‘subjective philosophy of probability.” We actually go on and on in our book about how Bayesian data analysis does not rely on subjective probability, but . . . “nothing in common,” huh? That’s pretty strong.
Rather than attempt to address the book’s arguments in general, I will simply do two things. First, I will do a “Washington read” (as Yair calls it) and see what Burdzy says about my own writings. Second, I will address the question of whether Burdzy’s arguments will have any effect on statistical practice. If the answer to the latter question is no, we can safely leave the book under review to the mathematicians and philosophers, secure in the belief that it will do little mischief.
Burdzy characterizes the discussion of philosophical issues in our book as “level headed and reasonable,” which is fair enough. He does criticize us for giving “too many philosophical arguments” and for sweeping the “fundamental philosophical problem of verification” under the rug, but that doesn’t bother me. Lots has been written on Bayesian philosophy, even by me, and we felt our best contribution in BDA would be to focus on methods, not on philosophical justifications.
Oddly enough, Burdzy at one point appears to criticize us for discussing subjectivity at all, on the grounds that “standard textbooks on chemistry do not discuss subjectivity in their introductions, and so statistical textbooks need not to do that either . . .” I’m tempted to reply with, “Gee, I’d never thought of it that way,” but after an earlier blog discussion I vowed to suppress sarcasm on the grounds that it could be misunderstood. So let me answer this straight by saying that statistics and chemistry are quite different subjects. There’s not discussion of isotopes or benzene rings in Bayesian Data Analysis, and no discussion of subjectivity and causality in chemistry textbooks. As a professor of political science, I’d just as well not have my textbooks constrained to be a subset of the chemistry curriculum.
Now to the question of what difference Burdzy’s book might make. The key point of the book, from my perspective, is its criticism of subjective Bayesian statistics–in Burdzy’s words, “the subjective theory does not imply the Bayes theorem.” That’s fine by me, but of course nothing new if you look at Bayesian Data Analysis, chapter 1 (most of which is unchanged from the original 1995 version). I have no problem with Burdzy writing about stuff that I’ve written on before–obviously, others such as George Box and E. T. Jaynes made similar points before we do–I just don’t think Burdzy’s claims are as earth-shaking as he apparently believes. (On the back cover, he claims “a radical departure from the current philosophical duality . . . the frequency and subjective theories.)
My guess is that Burdzy would differ very little from Christian Robert or myself when it comes to statistical practice. I believe it’s harmless for him to write about Bayesian philosophy–and maybe his book will even be helpful in communicating our ideas to mathematicians who’ve vaguely heard of Bayesian statistics and mistakenly associate it with subjectivity. Personally, I think this material is covered better in chapter 1 of Bayesian Data Analysis (with side trips to chapters 6, 7, and 8) or, if you want a more philosophical and argumentative perspective, with the appropriate chapters of Berger and Jaynes, but I suppose that different styles of presentation will be effective with different audiences.