Straw man design 101

One expects articles that appear in professional journals to be more polished and accurate than blog posts. So I waited with interest to see how Andrew Gelman's comments on my book published in his blog would change in the "final" version published in a scientific journal Bayesian Analysis. They appeared in vol. 5 (2010) as Comment on Article by Robert pp. 229 - 232. In what follows, I will refer to the version published in Bayesian Analysis.

Gelman writes in Section 2 "Rather than attempt to address the book's arguments in general, I will simply do two things. First, I will do a `Washington read' [...] 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."

Gelman does not pretend that his comments are a full scale review of my book - this is fair. It is also understandable that he replies to my comments on his book. I have already posted my reaction to his comments here. The discussion described so far deals mostly with opinions so I have no reason to be especially unhappy about it.

Gelman starts the second of the two themes of his comments with "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 [...]." Amazingly, the most substantial part of Gelman's comments is based on two falsehoods. And I do not mean the difference of opinions.

First, my book does not contain "criticism of subjective Bayesian statistics". Section 8.4.3 of my book starts with "A prior may represent scientist's prior knowledge in an informal way. Using such priors is a sound scientific practice [...]." I do criticize the subjective philosophy of probability invented by de Finetti elsewhere in the book but this is miles away from "criticism of subjective Bayesian statistics".

Second, "the subjective theory does not imply the Bayes theorem" is the title of Section 7.6 in my book, pp. 143-157. This rather long section shows that de Finetti-style axiomatic theories are too weak to imply the Bayes theorem. A good analogy would be an axiomatic system for mathematics that is too weak to imply the Pythagorean theorem. It is irrelevant whether Gelman thinks that my claim in Section 7.6 is true or false, significant or insignificant, interesting or not. What is relevant is that Gelman asserts that my claim appeared in Chapter 1 of Bayesian Data Analysis. In fact, Gelman's book does not contain any discussion of the logical strength of de Finetti-style axiomatic theories of probability.

Gelman created two straw men - one misrepresenting my book and one misrepresenting his book.