Another Feller theory

My paper with Christian Robert, “Not Only Defended But Also Applied”: The Perceived Absurdity of Bayesian Inference, was recently published in The American Statistician, along with discussions by Steve Fienberg, Steve Stigler, Deborah Mayo, and Wesley Johnson, and our rejoinder, The Anti-Bayesian Moment and Its Passing.

These articles revolved around the question of why the great probabilist William Feller, in his classic book on probability (“Feller, Volume 1,” as it is known), was so intemperately anti-Bayesian. We located Feller’s attitude within a post-WW2 “anti-Bayesian moment” in which Bayesian inference was perceived as a threat to the dominance of non-Bayesian methods, which were mature enough to have solved problems yet new enough to still appear to have limitless promise.

Howard Wainer read this. Howard is a friend who has a longstanding interest in the history of statistics and who also has known a lot of important statisticians over the years. Howard writes:

On Feller: I have another theory of his Bayesian antipathy (unlikely perhaps, but not impossible).

Tukey always maintained a dislike for Bayesian methods. This was far out of character, for he was a pragmatist and was delighted to use anything that would help. I couldn’t understand it, so the story I made up was that it was less an antipathy to Bayesian methods than it was for rigid Bayesians. While this might be true, the story told in “The Theory that would not die” provided another answer – that he viewed Bayesian methods as a state secret, akin to nuclear secrets of the Manhattan project. That letting out how useful they were would give a boost to America’s enemies (remember the mindset of the late 40s, the 50s and the 60s). This same issue, of a more mercantile nature, arose when he used Bayesian methods for election predictions for NBC. He must’ve felt that this is what gave NBC the edge over the other networks in the speed and accuracy of their projections and he forbade the other members of his prediction team to make public how they did it (check with Velleman or Fienberg for details).

While I don’t think that Feller was concerned much about NBC’s corporate secrets, he was certainly a patriot and might have stuck in some gratuitous slams into his book as a red herring to point ‘the enemy’ away from methods that could be a big help to them. The quality of the rest of his work is so high that it is hard to believe that he didn’t have a firm understanding of the limits of frequentist methods as well as the promise of Bayesian ones. Again, remember the mindset of post-WWII America (and the role that Princeton’s statisticians played in the war effort) and the red scare and the attitudes that allowed McCarthy. I wouldn’t gainsay this possibility.

I’m reminded of my fanciful theory about Linus Pauling and vitamin C. My theory is that Pauling believed in the placebo effect, and that this was his high-stakes attempt to create such an effect, basically leveraging his immense personal and scientific reputation so as to give people the belief that vitamin C really worked.