A caricature of Bayesian statistics

Following a rather shocking rendering of Bayesian statistics in the French popular Science magazine La Recherche last June by a French statistician, Nicolas Vayatis, I decided to send the following protest letter to its Editor as the ISBA president (my translation of a googslation, pardon my French!).

“As a statistician and as the current (2008) President of the International Society for Bayesian Analysis (ISBA), I would like to protest against the presentation and incredibly simplistic caricature made by Nicolas Vayatis of Bayesian statistics in No. 421 (p.26) of La Recherche.

Firstly, the Bayesian approach has not developed “along with the improvement of computers” but, rather, this approach has been dominant throughout the nineteenth century, from Laplace to Poincaré. Also, the contrast between Bayesian and frequent approaches is definitely not “philosophical”; on the opposite, it deals with the effectiveness and universality of procedures built therein.

Then, the presentation of Bayesian statistical inference made in the article got it all wrong: in the simple exemple of inference on the probability p of a coin hitting head during 100 tests on the same coin, the probability p also remains a “real” value, both unique and unknown, in the Bayesian approach which merely updates the [posterior] distribution of the probability parameter p given the number of heads obtained during the experiment. This probability distribution is not a belief but a rational construct that update information on p by integrating the pieces of information contained in the comments. Now this distribution is used to deduce an estimate of p as well as to test if the coin is biased or not.

Secondly, contrary to the title, the sectarian image spread by the paper (“mostly Anglo-Saxon”, “self-centered”, “Bayesian hymns”, “journals that do not accept the frequentist views”) decidedly is a thick-skinned caricature in the community even though it does not stand against examination: there are well-established Bayesian statisticians in many other countries than anglo-saxon countries, such as Chile, Brazil, Spain, or Italy, and obviously France. (For instance, a series of global conferences sees Bayesian statisticians gather every four years in Spain.) First-rate international journals of mathematical statistics, computational statistics or methodological statistics all include between 20% and 30% of Bayesian articles, they all have had Bayesian editors at one time or another, without a noticeable impact on or the quality of these journal. The only journal mostly devoted to Bayesian techniques is Bayesian Analysis, an electronic journal that was only recently created. Similarly, most national or international statistical societies have had or have chairs that are Bayesians and they apparently survived without collateral damage.

Finally, and it is indeed a story that did not belong in the article, the only Bayesian songs that you can hear at Bayesian conferences are those pastiches sung at the “cabaret” which concludes the conference banquet. This is a (indeed) Anglo-Saxon tradition of self-derision that is also found in many other conferences outside Bayesian statisticians.”

What is amazing is not that a popular Science magazine talks non-sense, this happens all the time (for instance, the same La Recherche confuses statististical Physics with Statistics in its September issue!). Nor is it the fact that editors build articles from browsing mostly at random ArXiv (this seems to be the case for most entries in the Mathematics section…), even though the current case is rather extreme (a communication made by a philosopher at a 2003 meeting that “focus on the pragmatic point of view of scientists’ day-to-day practices”, resulting in a poorly edited document that does not bring much novelty to the debate and further attributes Bayesian tendencies to Karl Popper). No, it is the illustration of the medias turning anyone and everyone into an expert without any checking and of those anyone and everyone gleefully endossing the expert coat (see all those so-called Economics experts unable to explain the impact of the subprime crisis on European banks, so we’d be better using sticky figures instead of experts)! In fact, in the current case, the expert is specialised in Machine Learning and non-parametric Statistics and he should know better about the basics of Bayesian Statistics… In any case, he is talking non-sense about Bayesians publishing in their own journals (like what?! Annals of Statistics? JASA? JRSS Series B?) and singing Bayesian anthems at the opening of their meetings (simply demonstrating he never attended a Bayesian meeting). This must be an effect of the expert’s self-intoxication of being able to make statements without any moderation by peers…