A video made in Padova:(and shown during a break at the workshop), watch out for Bayes’ theorem!
Archive for The Monty Hall problem
“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. Continue reading
The colloquium held today at Glasgow University in honour of Mike Titterington for his retiral was highly enjoyable! First, it was a pleasure to celebrate Mike’s achievements at this (early) stage of his career, along with people from Glasgow but also from all over the UK and even from Australia, among whom a lot of friends. Second, the (other) talks were highly interesting, with Peter Hall talking about the asymptotics of records, Byron Morgan about identifiability in capture-recapture models, Peter Green presenting a graphical diagnostic for spotting divergence between prior and likelihood in multivariate models, and Adrian Bowman illustrating advanced face analysis using principal curves on lips and faces. Third, I got a fair amount of questions and comments about ABC in general and ABC model choice in particular, including David Cox commenting that ABC was an important new topic and suggesting using goodness-of-fit tools for model comparison. The symposium per se ended up with a specially designed cake covering (in sugar!) some of Mike’s academic endeavours during the past years. While a formal affair for which I had to run to get a shirt, the diner was equally enjoyable, including a simultaneously witty and deep after-dinner talk paying tribute to Mike’s contributions by David Cox (who was Mike’s predecessor as editor of Biometrika) and a funny conclusion by John McColl who dug out a 1976 probability assignment he had from Mike that was the Monty Hall problem.
This little article contains nothing new, and only almost trivial mathematics. It is a plea for future generations to preserve the life of The True Monty Hall paradox, and not let themselves be misled by probability purists who say “you must compute a conditional probability”.
Richard Gill posted a paper on arXiv this morning about the Monty Hall problem. He does not mean to try yet another solution to the problem more susceptible to convince the army of skeptics out there, but rather to illustrate the hidden and implicit assumptions behind the mathematisation (sic!) of the problem… As a background to the problem, Richard Gill refers to the book The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser that led to my earlier post. Now, after having read the paper and come upon the final sentence reported above, I must say I am none the wiser about why the author wrote the paper! To me the Monty Hall problem is primarily an instance of wrong conditioning… Nonetheless, I appreciate the points about visualising the puzzle as a decision theoretic problem and the solution as the minimax procedure.