## Misconceptions on Bayesianism

**I**t seems to me that the most common attack against Bayesianism relates to its sectarian aspects. While unjustified, this criticism is grounded and long-lasting for several reasons. The first one is the Bayesian claim to universality: no other branch of Statistics attempts to cover so generically all branches of Statistics, from estimation to testing, from design to non-parametrics, from minimax theory to graphical modelling. That Bayesian principles can integrate so smoothly all kinds of statistical optimalities may feel like propaganda to non-Bayesians, even though there are many proofs of this efficiency, from consistency to admissibility, from Dutch-book arguments to exchangeability (see de Finetti).

**T**he second reason is that no other (major) approach to Statistics is so strongly anchored on philosophical principles. This deep connection with Philosophy sounds to me like a strong added value, in particular for analysing the nature of learning (see Savage and Dawid) and the influence of a prioris (back to Laplace and Poincaré), but the threads linking modern Statistics to Mathematics and to Informatics may make this additional link (and the argumentative discussions involved in some Bayesian papers) seem old-fashioned and un-scientific. (It is also true that the literature abounds with philosophical arguments that are not always of the highest quality, see for instance some of the introductory paragraphs of the nonetheless fundamental and foundational Theory of Probability!) The essential fact that a Bayesian analysis relies on the choice of a prior distribution inevitably opens the door to the sectarian criticism, even though it is as well an (the!) inevitable part of the Bayesian principles. That two different statistical analyses of the same data could conduct to two different conclusions is seen by some as a major default in the theory, while it seems unavoidable (see again Poincaré). The criticism is that the use of a prior is un-scientific or un-objective (or un-falsifiable in Popperian terms) and that this choice is based on tenets only understandable to members of the sect…

**A** third and related reason is that Bayesians have developed along the years a real sense of community. For one thing, no other (major) branch of Statistics has members so naturally gathered under a common denomination (e.g., likelihoodists?! Basu had dubbed the Indian construct likelihood-wallah on those using likelihood, but this has obviously not stuck! Fiducians could be the closest to this fame, but I am not even sure the name exists.) There are many good things in having a feeling of community and, as mentioned on Saturday, this includes real benefits in terms of collaborative research and in keeping the unitarian perspective of the statistical approach, but one drawback of communities is that people outside the community may naturally feel dismissive, ostracised, excluded, suspicious, jealous, or, in the most extreme cases, antagonistic and belligerent, i.e. anti-Bayesians. (This is a point shared with religions and sects, most obviously, that those not “in” are automatically “out”.) The fact that this community has also developed some traditions that could be dubbed “rituals”, like having meetings in sea resorts (in Spain and elsewhere), and alas rarely in cold and mountainous places (even though MCMC’ski could be the start of a new tradition!), with a strong emphasis on partying! Again, nothing wrong with adding a few extra good reasons to attending conferences, but this may not seem right to outsiders who have never attended a poster session at a Valencia meeting that starts in the hotel bar at 10am and ends up at two in the morning with people still loudly arguing around papers. Having launched ** Bayesian Analysis** was also a great idea, even though I remember it being fiercely debated at a Bayesian meeting (where I must admit I voted against it!), but it also strengthens the (wrong) impression of a closed group with its own agenda “only publishing in its own journals”.

**T**he last reason I want to point out is the fact that Bayesianism draws its name from one man, Thomas Bayes, and that, while there are good reasons for this filiation, this is also a feature shared with sects! As any other branch of Statistics, Bayesian theory has been built on the work of many and this singling out one person as the founder of the theory is unfortunate. Especially when considering that Bayes’ main posthumous work is not really in Statistics and was rediscovered by Laplace a few years later. While it seems a wee late to switch the denomination, I really think the abuse of the (maybe apocryphical) picture of the Reverend on our webpages and in our talks and of the corresponding cult of personality including caring for Bayes’ tomb in a London cemetery (!) should cease to be part of our attitude. It would certain help in reducing the sectarian libels.

**Ps**—The column Dr Fisher’s casebook in the recent December issue of Significance is quite representative of these misconceptions on Bayesianism, ranking Bayesians as born-again fundamentalists…

September 6, 2011 at 7:27 am

[…] well-attended) public lecture on the Bayesian nature of risk that made me think further about the de Finetti‘s “probability does not exist”, a declaration that had irked me until then. (And […]