## “la formule qui décrypte le monde”

“It is only in the 1980s that the American mathematician Judea Pearl has shown that, by aligning hundreds of Bayes formulas, it was possible to take into account the multiple causes of a complex phenomenon.”(my translation)

**A**s a curious coincidence, the latest issue of *Science & Vie* appeared on the day I was posting about Peter Coles’s warnings on scientific communication. The cover title of the magazine is the title of this post, *The formula decrypting the World*, and it is of course about… Bayes’ formula, no-one else’s!!! The major section (16 pages) in this French scientific vulgarization magazine is indeed dedicated to Bayesian statistics and even more Bayesian networks, with the usual stylistic excesses of journalism. As it happens, one of the journalists in charge of this issue came to discuss the topic with me a long while ago in Paris-Dauphine and I remember the experience as being not particularly pleasant since I had trouble communicating the ideas of Bayesian statistics in layman terms. In the end, this rather lengthy interview produced two quotes from me, one that could be mine (in connection with some sentences from Henri Poincaré) and another that is definitely apocryphal (yes, indeed, the one above! I am adamant I could not have mentioned Judea Pearl, whose work I am not familiar with, and even less this bizarre image of hundreds of Bayes’ theorems… Presumably, this got mixed up with a quote from another interviewed Bayesian. The same misquoting occurred for my friend Jean-Michel Marin!).

**A**mong the illustrations selected in the journal as vignettes, the Monty Hall paradox—which is an exercise in conditioning, not in statistical reasoning!—, signal processing for microscope images, Bayesian networks for robots, population genetics (and the return of the musk ox!), stellar cloud formation, tsunami prediction, microarray analysis, climate meta-analysis (with a quote from Noel Cressie), post-Higgs particle physics, ESP studies invalidation by Wagenmakers (missing the fact that the reply by Bern, Utts, and Johnson is equally Bayesian), quantum physics. From a more remote perspective, those are scientific studies using Bayesian statistics to establish important and novel results. However, it would have been easy to come up with equally important and novel results demonstrated via classical non-Bayesian approaches, such as exhibiting the Higgs boson. Now, I understand the difficulty in conveying to the layman the difference resulting from using a Bayesian reasoning to support a scientific argument, however this accumulation of superlatives opens the door to suspicions of bias and truncated perspectives… The second half of the report is less about statistics and more about psychology and learning, expanding on the notion that the brain operates in ways similar to Bayesian learning and networks.

“Bayes’ little formula went a long way from the dusty statistical chapter where it had been relegated. By unveiling the sesame of the way our thought process operates, it promises nothing less than to reveal the secret that defines humanity.”(my translation)

**W**hat somehow annoys me with this kind of coverage is that it is excessive and therefore a-scientific in this excess: “revolution”, “harvest of discoveries and inventions”, “the formula that decrypts every mystery of Nature”, “the formula of thinking in action”, “a staggering efficiency”, “a miraculous tool”, “a magic formula”, “the Bayesian tsunami”, &tc. While I do think that a Bayesian approach to statistical issues is both more efficient and more coherent, I would certainly not engage in this kind of discourse, simply because it sounds sectarian rather than rational (and furthermore because Bayesians have been charged quite a lot with indulging in this kind of behaviour!). Now, some of the arguments reported in the text are quite convincing for me, like the inclusion of subjective beliefs and the ability to weight models and theories. Overall, it provides an entry to newbies into a field and stresses the appeal of a statistical tool in scientific induction, a tool so often missing from the toolbox of many scientists. Still, I feel uneasy about the global message transmitted by the journal. making Bayes’ formula sounding too much like a formula from Harry Potter!!!

November 7, 2012 at 2:59 pm

Thanks Christian for your pertinent comments on this article published in the last issue of Sciences & Vie which I greatly agree with.

As regards of popularization of science especially in the field of statistics, to be honest we have to recognize that the task is far from being easy at all at any level you consider it.

The article by Martine Fontez and Roman Ikonikoff entitled “the formula that deciphers the world” is not exempt of the usual impediments and failings of this kind of journalism primarily emphasizing sensational aspects of science and techniques. To that respect, there is a big gap between this attempt of popularizing Bayesian statistics and the one made by Sharon Bertsch McGrayne in her recent book “the theory that would not die” summarized in lectures eg http://www.channels.com/episodes/show/14898621/Authors-Google-Sharon-Bertsch-Mc-Grayne

which has the great merit to put the issue in the historical and sociological contexts of statistics with many significant examples and without any mathematical technicality.

The idea that the Bayesian theory is something straightforward is also somewhat misleading. I remember this sentence of DA Berry (1997) quoted by Bruno Lecoutre in his lecture “Teaching Bayesian statistics to beginners” at Applibugs, Nov 26, 2009: “Bayesian statistics is difficult in the sense that thinking is difficult”.

I would add : especially when thinking in terms of probability, this part of mathematics requiring very subtle ways of reasoning as well shown by the example shown by Fontez et al of the “Monty Hall problem” the answer to which is not at all intuitive. Having specialized in quantitative genetics, I remember how enlightening were Albert Jacquard’s book and courses but also how painful was at start our adaptation to his probabilistic views of population genetics as compared to the usual one based on “gamete tables” .

Despite that, I found the article worth reading as it emphasizes very well the great interest arising now in Bayesian statistics coming from many different fields including psychological and cognitive sciences: see works and courses of Stanilas Dehaene at College de France.

Good luck for your talk next Friday afternoon on France Culture I will certainly not miss.

November 6, 2012 at 10:33 pm

Quick question: in your experience, how many hours should be set aside in an engineering school curriculum to open the students’ mind to statistics (ideally with a Bayesian twist) ? In particular, for the French system, do you think it should be taught in prepas or in the engineering schools aferwards.

November 6, 2012 at 10:39 pm

thanks! In my opinion it should nOt be taught in prepas as (a) the students do no get a proper training in probability and (b) the professors are not trained in either probability or statistics. For engineer schools, a fill semester course on statistical techniques, whether Bayesian or frequentist, seems like the minimum minimorum…!

November 10, 2012 at 4:47 pm

You mean a full semester course as in US universities i.e. 3 hours / week + homework for 3 months ?

November 6, 2012 at 11:26 am

As a layman person generally interested in scientific ideas and their applications, it struck me how well Bayes theory seems to fit into the probabilistic nature of quantum mechanics for example. Or how well it consolidates subjective and objective approaches in reasoning and this in a consistent mathematical fashion. This is what might one lead to think, that Bayes could provide a tool for a group of people to come to a common understanding. I think that can be quite inspiring also to people who are not scientists?!

November 6, 2012 at 9:20 am

it seems this is not over: I am now invited to discuss Bayes formula on the French national radio, in company with other researchers interviewed in this paper…. Still in an inflated journalistic mode: “Is there a universal mathematical formula?”…

November 10, 2012 at 4:49 pm

Just tell them the truth: No.