A video made in Padova:(and shown during a break at the workshop), watch out for Bayes’ theorem!
Archive for Bayes theorem
While running this morning I was reconsidering (over and over) my discussion of Bayes’ formula on the radio and thought I should have turned the presentation of Bayes’ theorem differently. I spent much too much time on the math side of Bayes’ formula and not enough on the stat side. The math aspect is not of real importance as it is a mere reformulation of conditional probabilities. The stat side is what matters as introducing a (prior) distribution on the parameter (space) is the #1 specificity of Bayesian statistics…. And the focus point of most criticisms, as expressed later by the physicist working on the Higgs boson, Dirk Zerwas.
I also regret not mentioning that Bayes’ formula was taught in French high schools, as illustrated by the anecdote of Bayes at the bac. And not reacting at the question about Bayes in the courtroom with yet another anecdote of Bayes’ formula been thrown out of the accepted tools by an English court of appeal about a year ago. Oh well, another argument for sticking to the written world.
In relation with the special issue of Science & Vie on Bayes’ formula, the French national radio (France Culture) organised a round table with Pierre Bessière, senior researcher in physiology at Collège de France, Dirk Zerwas, senior researcher in particle physics in Orsay, and Hervé Poirier, editor of Science & Vie. And myself (as I was quoted in the original paper). While I am not particularly fluent in oral debates, I was interested by participating in this radio experiment, if only to bring some moderation to the hyperbolic tone found in the special issue. (As the theme was “Is there a universal mathematical formula? “, I was for a while confused about the debate, thinking that maybe the previous blogs on Stewart’s 17 Equations and Mackenzie’s Universe in Zero Words had prompted this invitation…)
As it happened [podcast link], the debate was quite moderate and reasonable, we discussed about the genesis, the dark ages, and the resurgimento of Bayesian statistics within statistics, the lack of Bayesian perspectives in the Higgs boson analysis (bemoaned by Tony O’Hagan and Dennis Lindley), and the Bayesian nature of learning in psychology. Although I managed to mention Poincaré’s Bayesian defence of Dreyfus (thanks to the Theory that would not die!), Nate Silver‘s Bayesian combination of survey results, and the role of the MRC in the MCMC revolution, I found that the information content of a one-hour show was in the end quite limited, as I would have liked to mention as well the role of Bayesian techniques in population genetic advances, like the Asian beetle invasion mentioned two weeks ago… Overall, an interesting experience, maybe not with a huge impact on the population of listeners, and a confirmation I’d better stick to the written world!
“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)
As 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!).
Among 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. Read more »
Today, our reply to the discussion of our American Statistician paper “Not only defended but also applied” by Stephen Fienberg, Wes Johnson, Deborah Mayo, and Stephen Stiegler,, was posted on arXiv. It is kind of funny that this happens the day I am visiting Iowa State University Statistics Department, a department that was formerly a Fisherian and thus anti-Bayesian stronghold. (Not any longer, to be sure! I was also surprised to discover that before the creation of the department, Henry Wallace, came to lecture on machine calculations for statistical methods…in 1924!)
The reply to the discussion was rewritten and much broadened by Andrew after I drafted a more classical point-by-point reply to our four discussants, much to its improvement. For one thing, it reads well on its own, as the discussions are not yet available on-line. For another, it gives a broader impact of the discussion, which suits well the readership of The American Statistician. (Some of my draft reply is recycled in this post.)