Archive for Cédric Villani

Théorème vivant

Posted in Books, University life with tags , , , , , , , on November 7, 2012 by xi'an

When I ordered this book, Théorème Vivant (Alive Theorem), by Cédric Villani, I had misgivings about it being yet another illustration of the, pardon my French!, universal “pipolisation” process that turns values upside down and sets mundane aspects of major contemporary figures above their true achievements like, say, winning a Fields medal! However, as soon as I started reading Théorème Vivant, I realised it was a fascinating delve into the way mathematicians operate and how they build theorems. Of course, as an “insider”, I can find many entry points to relate to, some quite mundane and unrelated like entering the common room of a conference centre in the middle of the night to “steal” some life-saving tea bags or an aversion to taxi rides, not mentioning an addiction to French cheeses… And I have the advantage of being able to read the math formulas given in the book (even though this is not at all my area of expertise and I find the wording of the theorems and proofs rather unusual at times). But I think Théorème Vivant can be read by non-mathematicians as well, provided they take those formulas and paper extracts as pictures, just like the drawings of mathematicians interspeded throughout the book and do not get annoyed at not understanding the meaning of them (I do not get the deepest levels either!). Nothing to be afraid of: Théorème Vivant is another impressive illustration of the ability of Cédric Villani to explain mathematics to the general public and to surf upon his popularity with the medias. (The book is currently available in French only, but should soon be translated into English. Possibly polishing the least politically correct statements…) Continue reading

ABC in Le Monde?

Posted in Books, pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , on October 29, 2012 by xi'an

In the plane to Chicago, while being stuck on the tarmac at Roissy airport for an hour, I went through my newspapers, only to have the pleasant surprise find in the science leaflet of Le Monde that my co-author Arnaud Estoup, senior researcher at INRA in Montpellier (CBGP), was mentioned in a full page article for his work on the multi-colored Asian lady beetle (Harmonia axyridis, HA), establishing “that the recent burst of worldwide invasions of HA followed a bridgehead scenario, in which an invasive population in eastern North America acted as the source of the colonists that invaded the European, South American and African continents, with some admixture with a biocontrol strain in Europe“. Obviously, Le Monde does not goes as far as mentioning ABC, which was used in our paper to compare scenarios, i.e. to make ABC model choice! (I may also add that the invasion of those Asian bettles in our neighbourhood is a real nuisance and, each Fall, I keep checking for any sign of black beetles inside the house before disaster strikes…)

Despite an inauspicious start (RER B train finishing its trip in Paris and forcing me to board in a hurry a taxi to the airport, abyssal mess at Roissy airport [now, that’s a surprise!], departure delayed by 90 minutes), I got some work done during the nine hour flight, including reading and reviewing a PhD thesis, and I even managed to get my connection from Chicago to Des Moines despite a tight 45 minutes transfer time! At a personal level, this reminded me of the very first time I flew to the US, in August 1987, as it also was through O’Hare and I also had to rush to get my connection to Lafayette, Indiana. Even more anecdotally, this AF0664 flight from Paris to Chicago happened to be the very last one, as the route is discontinued by Air France. The second flight to Des Moines was on a small propeller plane and, despite sitting next to an obnoxious drunk woman who wanted me to know everything about her [dull, so very dull] life, quite pleasant: I finished reading in the Midwest sun the highly entertaining thriller by Cédric Villani, Le Théorème vivant. (Obviously soon to be reviewed on The ‘Og!)

estimating a constant (not really)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on October 12, 2012 by xi'an

Larry Wasserman wrote a blog entry on the normalizing constant paradox, where he repeats that he does not understand my earlier point…Let me try to recap here this point and the various comments I made on StackExchange (while keeping in mind all this is for intellectual fun!)

The entry is somehow paradoxical in that Larry acknowledges (in that post) that the analysis in his book, All of Statistics, is wrong. The fact that “g(x)/c is a valid density only for one value of c” (and hence cannot lead to a notion of likelihood on c) is the very reason why I stated that there can be no statistical inference nor prior distribution about c: a sample from f does not bring statistical information about c and there can be no statistical estimate of c based on this sample. (In case you did not notice, I insist upon statistical!)

To me this problem is completely different from a statistical problem, at least in the modern sense: if I need to approximate the constant c—as I do in fact when computing Bayes factors—, I can produce an arbitrarily long sample from a certain importance distribution and derive a converging (and sometimes unbiased) approximation of c. Once again, this is Monte Carlo integration, a numerical technique based on the Law of Large Numbers and the stabilisation of frequencies. (Call it a frequentist method if you wish. I completely agree that MCMC methods are inherently frequentist in that sense, And see no problem with this because they are not statistical methods. Of course, this may be the core of the disagreement with Larry and others, that they call statistics the Law of Large Numbers, and I do not. This lack of separation between both notions also shows up in a recent general public talk on Poincaré’s mistakes by Cédric Villani! All this may just mean I am irremediably Bayesian, seeing anything motivated by frequencies as non-statistical!) But that process does not mean that c can take a range of values that would index a family of densities compatible with a given sample. In this Monte Carlo integration approach, the distribution of the sample is completely under control (modulo the errors induced by pseudo-random generation). This approach is therefore outside the realm of Bayesian analysis “that puts distributions on fixed but unknown constants”, because those unknown constants parameterise the distribution of an observed sample. Ergo, c is not a parameter of the sample and the sample Larry argues about (“we have data sampled from a distribution”) contains no information whatsoever about c that is not already in the function g. (It is not “data” in this respect, but a stochastic sequence that can be used for approximation purposes.) Which gets me back to my first argument, namely that c is known (and at the same time difficult or impossible to compute)!

Let me also answer here the comments on “why is this any different from estimating the speed of light c?” “why can’t you do this with the 100th digit of π?” on the earlier post or on StackExchange. Estimating the speed of light means for me (who repeatedly flunked Physics exams after leaving high school!) that we have a physical experiment that measures the speed of light (as the original one by Rœmer at the Observatoire de Paris I visited earlier last week) and that the statistical analysis infers about c by using those measurements and the impact of the imprecision of the measuring instruments (as we do when analysing astronomical data). If, now, there exists a physical formula of the kind

c=\int_\Xi \psi(\xi) \varphi(\xi) \text{d}\xi

where φ is a probability density, I can imagine stochastic approximations of c based on this formula, but I do not consider it a statistical problem any longer. The case is thus clearer for the 100th digit of π: it is also a fixed number, that I can approximate by a stochastic experiment but on which I cannot attach a statistical tag. (It is 9, by the way.) Throwing darts at random as I did during my Oz tour is not a statistical procedure, but simple Monte Carlo à la Buffon…

Overall, I still do not see this as a paradox for our field (and certainly not as a critique of Bayesian analysis), because there is no reason a statistical technique should be able to address any and every numerical problem. (Once again, Persi Diaconis would almost certainly differ, as he defended a Bayesian perspective on numerical analysis in the early days of MCMC…) There may be a “Bayesian” solution to this particular problem (and that would nice) and there may be none (and that would be OK too!), but I am not even convinced I would call this solution “Bayesian”! (Again, let us remember this is mostly for intellectual fun!)

Mathematics on public radio

Posted in University life with tags , , , , , on September 5, 2010 by xi'an

Following the Field medals awarded to Cédric Villani (the head of IHP and a former Dauphine PhD, as our president quickly communicated about) and Ngô Bao Châu (formely at Orsay, now moving to Chicago a fact omitted on the local news!), the French public radio, France Inter, dedicated one of its evening phone debates (Le Telephone Sonne) to research in Mathematics. The panelists were Cédric Villani, Jean-Pierre Bourguignon (head of IHES), and Guy Métivier (head of Mathematics at CNRS). This actually happens rather often (i.e. more often than once every four years when a French mathematician gets a Field medal) and I came across several of those by happenstance. The exercise (explaining to the layman what is the meaning of doing research in Mathematics and what are the advances made by the medalists in the current case) is interesting if delicate as the temptations to get lyrical or technical abound! I found the panelists did a very good job last Wednesday night. (Note that Terry Tao gave a summary of the four panelists’ achievements on his blog.) A very sweet (and my preferred) question was whether or not mathematical objects/concepts have an existence of their own or are created in mathematicians’ minds. In linking pure and applied maths, ie stating that there was no frontier between the two and that pure mathematicians are often involved in fruitful applications, Cédric Villani even mentioned Statistics, which is nice even though I doubt there is the remotest chance a statistician could get the Field Medal. (Incidentally, the COPSS Award, which is the Field Medal of Statistics, was attributed to David Dunson, from Duke, last August. Well-deserved, David!)