I’ve been reading a bunch of papers on Bayesian statistical inference lately, somewhat to my regret. I have no particular objection to Bayesian statistics, but distressingly often, a Bayesian paper will include a gratuitous slam of all other types of statistics. D. V. Lindley’s papers (which are classics in the literature) are particularly noxious in this regard. It’s a strange pattern, and I’d be curious to know the history of the habit.

More pleasant is a paper by Brad Efron based on an address he gave at Phystat2003, Bayesians, Frequentists, and Physics, which offers a detente in the Bayesian-frequentist debate. He describes Stein’s paradox, which is a challenge from both the Bayesian and classical points of view, and discusses means of inference, such as empirical Bayes, which are (arguably) neither purely Bayesian nor purely frequentist.

As someone who trained in math statistics, I can tell you the debates between frequentists and bayesians have at times been very hostile. I think the personal abuse in statistics can be traced to Ronald Fisher (who was a sort of frequentist), who was notorious for the personal nastiness of his comments on the work of others, although he was usually arguing with fellow frequentists. As recently as 2000, I have seen famous frequentists and bayesians clash at a conference, with the session chair having to intervene to stop more personal abuse being hurled. (Sample: “I have studied this subject for over 20 years, and I still cannot make coherent sense of your position.” Reply: “It is not our fault if you are slow to understand basic concepts.”)

In general, I would say that most statisticians were and are pragmatic, interested in whatever works, rather than in pursuing an ideological agenda. In such a community, it becomes relatively easy for a group of ideologically-driven people, such as the early bayesians (eg, James Savage, Dennis Lindley), to impose their will on the community.

There is a nice PhD thesis by Greg Wilson, of Los Alamos National Laboratory, looking at how the bayesians rose to prominence in math statistics. (Unfortunately, I don’t know of a copy online).

author = “Gregory D. Wilson”,

title = “Articulation Theory and Disciplinary Change: Unpacking the Bayesian-Frequentist Paradigm Conflict in Statistical Science”,

school = “Rhetoric and Professional Communication, New Mexico State University”,

year = “2001”,

type = “PhD”,

address = “Las Cruces, NM, USA”}

One explanation that occurred to me was “it’s all Fisher’s fault”, since Fisher was fairly notorious for his attacks on both his fellow frequentists and Bayesians, since once an argument gets heated, it rarely cools down. But if the conflict between frequentists and Bayesians is symmetric, frequentists are better at keeping it out of their papers.