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.

I would prefer someone like Ramsay – who did contribute productively to both philosopy and probability.

Ian Hacking, I believe lost interest in probability.

There is a risk to reading work by those who may have inadequate background …

Keith

"whether Burdzy's arguments will have any effect on statistical practice"

Judging by the comments on his blog (precisely zero since it started in June), and the reviews on Amazon (also zero), I think it is safe to say his arguments are likely to have very little effect on statistical practise. Charging $55 for a 272 page book doesn't help either.

Simon: What I was referring to was the possible effect on statistical practice of this book, were it to achieve wide circulation. If I thought said effect could be malign, I would've engaged more with the positive arguments of the book. As it was, though, I felt that Burdzy's positive arguments were reasonable (if unexceptional), even if his criticisms of others were way off-base.

[Side note for the curious re: "Devil" lede] Spacey's Verbal Kint in

The Usual Suspectslikely invoked Baudelaire's sentiment from his short story "The Generous Gambler."Andrew,

I posted a reply to your remarks on chemistry and statistics textbooks on my blog. The reason for the change of venue is that I use my blog to collect thoughts that might be reused at some later time, say, to give a talk. All my previous comments posted on your and Robert's blogs were "general remarks".

Chris

Andrew,

I read the updated version of your review of my book, "The Search for Certainty", to appear in "Bayesian Analysis". I would like to clarify one point. You quote me as saying that

(7.6) "The subjective theory does not imply the Bayes theorem."

I call it (7.6) because it is the title of Section 7.6 in my book (pages 143-157). Then you add in your review: "That's fine by me, but of course nothing new if you look at `Bayesian Data Analysis', Chapter 1." I read Chapter 1 of BDA before publishing my book and I have just refreshed my memory (using Google Books) and I still do not see where a claim identical or similar to (7.6) appears in Chapter 1 of BDA. Could you please give me page and line reference?

What makes this even more mysterious to me is a remark in your own comment in your blog:

(A) "subjective probability is Bayesian, but, no, Bayesian probability does not have to be subjective".

Statement (7.6) and the first part of (A) contradict each other, and you seem to support both. If there is an explanation for the (apparent) contradiction, I would be interested in it.

For the readers who do not have time and patience to read Section 7.6 of my book, let me give a brief summary of (7.6) and a link to an online resource. Sect. 7.6 shows a weakness in de Finetti-type formal theories. If you do not assume that objective probability exists, and you start with assumptions about rational decision making (using either a "Dutch book" argument or an axiomatic system) then you can prove that (i) decisions made before you collect the data should be coordinated using a probability distribution ("prior") and (ii) decisions made after the data are collected should be coordinated using a probability distribution ("posterior"). De Finetti-type theories are too weak to prove that the prior and the posterior should be coordinated using the Bayes theorem. In other words, these types of theories do not provide a link between a mathematical theorem (Bayes theorem) and applications. Slides for my talk on this topic are posted online in two formats, PowerPoint and PDF.

I am surprised by your claim that (7.6) is (in some form) in Chapter 1 of BDA because all you seem to say about axiomatic systems is that they are "suggestive but not compelling" (item 2 on page 13). BDA does not seem to go into deep analysis of their logical power.

Finally, yes, I know that (7.6) is irrelevant to statistics. But some people care not only about statistics but also about philosophy. (7.6) shows that de Finetti's theory has an extra weakness that seems to have been unnoticed before. To this day, some people write articles on new versions of de Finetti-style axiomatic systems. (7.6) may be irrelevant to your work but it is relevant to some currently done theoretical research.

Chris