Archive for Henri Poincaré

Red & Black Light [Ibrahim Maalouf]

Posted in Books, Mountains, pictures, Travel with tags , , , , on December 10, 2016 by xi'an

This morning I heard the trumpeter Ibrahim Maalouf speak on the French national public radio on his music, concerts, improvisation, Charlie friends, Poincaré (on intuition), and then I came upon this video, trailer for the movie In the Forests of Siberia, stunning. Especially the scene of the truck on the frozen lake with veins of white. And great trumpet music. (Admittedly biased views, since trumpet was my instrument.)

optimal simulation on a convex set

Posted in R, Statistics with tags , , , , , , on February 4, 2016 by xi'an

La Défense, from Paris-Dauphine, May 2009This morning, we had a jam session at the maths department of Paris-Dauphine where a few researchers & colleagues of mine presented their field of research to the whole department. Very interesting despite or thanks to the variety of topics, with forays into the three-body problem(s) [and Poincaré‘s mistake], mean fields for Nash equilibrium (or how to exit a movie theatre), approximate losses in machine learning and so on. Somehow, there was some unity as well through randomness, convexity and optimal transport. One talk close to my own interests was obviously the study of simulation within convex sets by Joseph Lehec from Paris-Dauphine [and Sébastien Bubeck & Ronen Eldan] as they had established a total variation convergence result at a speed only increasing polynomially with the dimension.  The underlying simulation algorithm is rather theoretical in that it involves random walk (or Langevin corrected) moves where any excursion outside the convex support is replaced with its projection on the set. Projection that may prove pretty expensive to compute if the convex set is defined for instance as the intersection of many hyperplanes. So I do not readily see how the scheme can be recycled into a competitor to a Metropolis-Hastings solution in that the resulting chain hits the boundary from time to time. With the same frequency over iterations. A solution is to instead use Metropolis-Hastings of course, while another one is to bounce on the boundary and then correct by Metropolis-Hastings… The optimal scales in the three different cases are quite different, from √d in the Metropolis-Hastings cases to d√d in the projection case. (I did not follow the bouncing option to the end, as it lacks a normalising constant.) Here is a quick and not particularly helpful comparison of the exploration patterns of both approaches in dimension 50 for the unit sphere and respective scales of 10/d√d [blue] and 1/√d [gold].

beyond subjective and objective in Statistics

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on August 28, 2015 by xi'an

“At the level of discourse, we would like to move beyond a subjective vs. objective shouting match.” (p.30)

This paper by Andrew Gelman and Christian Hennig calls for the abandonment of the terms objective and subjective in (not solely Bayesian) statistics. And argue that there is more than mere prior information and data to the construction of a statistical analysis. The paper is articulated as the authors’ proposal, followed by four application examples, then a survey of the philosophy of science perspectives on objectivity and subjectivity in statistics and other sciences, next to a study of the subjective and objective aspects of the mainstream statistical streams, concluding with a discussion on the implementation of the proposed move. Continue reading

failures and uses of Jaynes’ principle of transformation groups

Posted in Books, Kids, R, Statistics, University life with tags , , , , on April 14, 2015 by xi'an

This paper by Alon Drory was arXived last week when I was at Columbia. It reassesses Jaynes’ resolution of Bertrand’s paradox, which finds three different probabilities for a given geometric event depending on the underlying σ-algebra (or definition of randomness!). Both Poincaré and Jaynes argued against Bertrand that there was only one acceptable solution under symmetry properties. The author of this paper, Alon Drory, argues this is not the case!

“…contrary to Jaynes’ assertion, each of the classical three solutions of Bertrand’s problem (and additional ones as well!) can be derived by the principle of transformation groups, using the exact same symmetries, namely rotational, scaling and translational invariance.”

Drory rephrases as follows:  “In a circle, select at random a chord that is not a diameter. What is the probability that its length is greater than the side of the equilateral triangle inscribed in the circle?”.  Jaynes’ solution is indifferent to the orientation of one observer wrt the circle, to the radius of the circle, and to the location of the centre. The later is the one most discussed by Drory, as he argued that it does not involve an observer but the random experiment itself and relies on a specific version of straw throws in Jaynes’ argument. Meaning other versions are also available. This reminded me of an earlier post on Buffon’s needle and on the different versions of the needle being thrown over the floor. Therein reflecting on the connection with Bertrand’s paradox. And running some further R experiments. Drory’s alternative to Jaynes’ manner of throwing straws is to impale them on darts and throw the darts first! (Which is the same as one of my needle solutions.)

“…the principle of transformation groups does not make the problem well-posed, and well-posing strategies that rely on such symmetry considerations ought therefore to be rejected.”

In short, the conclusion of the paper is that there is an indeterminacy in Bertrand’s problem that allows several resolutions under the principle of indifference that end up with a large range of probabilities, thus siding with Bertrand rather than Jaynes.

Ulam’s grave [STAN post]

Posted in Books, Kids, pictures, Travel, University life with tags , , , , , , , on July 27, 2014 by xi'an

ulamSince Stan Ulam is buried in Cimetière du Montparnasse, next to CREST, Andrew and I paid his grave a visit on a sunny July afternoon. Among elaborate funeral constructions, the Aron family tomb is sober and hidden behind funeral houses. It came as a surprise to me to discover that Ulam had links with France to the point of him and his wife being buried in Ulam’s wife family vault. Since we were there, we took a short stroll to see Henri Poincaré’s tomb in the Poincaré-Boutroux vault (missing Henri’s brother, the French president Raymond Poincaré). It came as a surprise that someone had left a folder with the cover of 17 equations that changed the World on top of the tomb). Even though the book covers Poincaré’s work on the three body problem as part of Newton’s formula. There were other mathematicians in this cemetery, but this was enough necrophiliac tourism for one day.


Luke and Pierre at big’MC

Posted in Linux, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on May 19, 2014 by xi'an

crossing Rue Soufflot on my way to IHP from Vieux Campeur, March 28, 2013Yesterday, Luke Bornn and Pierre Jacob gave a talk at our big’MC ‘minar. While I had seen most of the slides earlier, either at MCMski IV,  Banff, Leuven or yet again in Oxford, I really enjoyed those talks as they provided further intuition about the techniques of Wang-Landau and non-negative unbiased estimators, leading to a few seeds of potential ideas for even more potential research. For instance, I understood way better the option to calibrate the Wang-Landau algorithm on levels of the target density rather than in the original space. Which means (a) a one-dimensional partition target (just as in nested sampling); (b) taking advantage of the existing computations of the likelihood function; and (b) a somewhat automatic implementation of the Wang-Landau algorithm. I do wonder why this technique is not more popular as a default option. (Like, would it be compatible with Stan?) The impossibility theorem of Pierre about the existence of non-negative unbiased estimators never ceases to amaze me. I started wondering during the seminar whether a positive (!) version of the result could be found. Namely, whether perturbations of the exact (unbiased) Metropolis-Hastings acceptance ratio could be substituted in order to guarantee positivity. Possibly creating drifted versions of the target…

One request in connection with this post: please connect the Institut Henri Poincaré to the eduroam wireless network! The place is dedicated to visiting mathematicians and theoretical physicists, it should have been the first one [in Paris] to get connected to eduroam. The cost cannot be that horrendous so I wonder what the reason is. Preventing guests from connecting to the Internet towards better concentration? avoiding “parasites” taking advantage of the network? ensuring seminar attendees are following the talks? (The irony is that Institut Henri Poincaré has a local wireless available for free, except that it most often does not work with my current machine. And hence wastes much more of my time as I attempt to connect over and over again while there.) Just in connection with IHP, a video of Persi giving a talk there about Poincaré, two years ago:

Bayes on the radio

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , on November 10, 2012 by xi'an

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!