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.

10 thoughts on “Another Feller theory

  1. Maybe Feller just thought Bayes was bunk. Then again, maybe he was an alien sent here to keep us on the wrong track. I would assign a much higher prior probability to the former explanation, but that seems sacrilegious somehow when done in reference to Feller.

  2. A major example of the danger of freely publishing conceptual breakthroughs during the Cold War was that Lockheed got the idea for the Stealth Fighter from an abstruse article in a Soviet technical journal. Wikipedia writes:

    “Modern stealth aircraft first became possible when Denys Overholser, a mathematician working for Lockheed Aircraft during the 1970s, adopted a mathematical model developed by Petr Ufimtsev, a Russian scientist …”

    Stealth technology gave the U.S. a huge step forward in its air superiority that emerged in the early 1980s, which terrified the Russian Air Force into backing Mikhail Gorbachev for the top job, which ultimately brought down the Soviet Union.

    • No. The Soviet Union collapsed because of its chronically under-performing agricultural sector and a one sided arms race they started in the early 1970s. The inherent weaknesses of the planned economy was laid bare after oil prices started falling in the mid 1980s. They could no longer cover the shortfalls in the other sectors by exporting raw materials and importing wheat and technology. The whole thing was going to come unglued no matter what kinds of fighter planes Lockheed built. Gorbachev made a difference because he decided to let Eastern Europe go its own way instead of shooting a whole bunch of Poles and Hungarians. Go read Stephen Kotkin’s Armagedon Averted.

  3. Andrew
    I think you’ve overlooked the anti bayesians who are still alive and well in Econometrics departments. Amazing how large
    sample asymptotics is so important in a field where there are no repeated experiments.

    Apologies to your coauthor but I tend to think the preponderance of rigid and complex frequentist methods in econometrics is possibly due to the French school which as we know is known for its oftentimes formal (Bourbakist) and dogmatic approaches to proof. That being said there are plenty of American econometricians whose frequentist approaches to timeseries verge on the absurd.

    But why is that?

    (and while you’re at it maybe you can explain why they like Gauss as opposed to the clearly superior R/SPlus and Matlab!).

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