Archive for bois de Boulogne

O’Bayes in action

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , on November 7, 2017 by xi'an

My next-door colleague [at Dauphine] François Simenhaus shared a paradox [to be developed in an incoming test!] with Julien Stoehr and I last week, namely that, when selecting the largest number between a [observed] and b [unobserved], drawing a random boundary on a [meaning that a is chosen iff a is larger than this boundary] increases the probability to pick the largest number above ½2…

When thinking about it in the wretched RER train [train that got immobilised for at least two hours just a few minutes after I went through!, good luck to the passengers travelling to the airport…] to De Gaulle airport, I lost the argument: if a<b, the probability [for this random bound] to be larger than a and hence for selecting b is 1-Φ(a), while, if a>b, the probability [of winning] is Φ(a). Hence the only case when the probability is ½ is when a is the median of this random variable. But, when discussing the issue further with Julien, I exposed an interesting non-informative prior characterisation. Namely, if I assume a,b to be iid U(0,M) and set an improper prior 1/M on M, the conditional probability that b>a given a is ½. Furthermore, the posterior probability to pick the right [largest] number with François’s randomised rule is also ½, no matter what the distribution of the random boundary is. Now, the most surprising feature of this coffee room derivation is that these properties only hold for the prior 1/M. Any other power of M will induce an asymmetry between a and b. (The same properties hold when a,b are iid Exp(M).)  Of course, this is not absolutely unexpected since 1/M is the invariant prior and since the “intuitive” symmetry only holds under this prior. Power to O’Bayes!

When discussing again the matter with François yesterday, I realised I had changed his wording of the puzzle. The original setting is one with two cards hiding the unknown numbers a and b and of a player picking one of the cards. If the player picks a card at random, there is indeed a probability of ½ of picking the largest number. If the decision to switch or not depends on an independent random draw being larger or smaller than the number on the observed card, the probability to get max(a,b) in the end hits 1 when this random draw falls into (a,b) and remains ½ outside (a,b). Randomisation pays.

unusual view of my office [jatp]

Posted in pictures, Travel with tags , , , , , , , , on October 18, 2017 by xi'an

Paris-Dauphine in Nature

Posted in Statistics with tags , , , , , , , , , on April 25, 2017 by xi'an

Since this is an event unlikely to occur that frequently, let me point out that Université Paris-Dauphine got a nominal mention in Nature of two weeks ago, through an article covering the recent Abel Prize of Yves Meyer and his work on wavelets through a collection of French institutions, including Paris-Dauphine where he was a professor in the maths department (CEREMADE) from 1985 till 1996. (Except for including a somewhat distantly related picture of an oscilloscope and a mention of the Higgs boson, the Nature article is quite nice!)

sunset from my office

Posted in pictures, University life with tags , , , , on November 10, 2015 by xi'an

fog lifting by mid-afternoon

Posted in pictures, University life with tags , , , , , , , on November 2, 2015 by xi'an

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from my office

Posted in pictures, Travel, University life with tags , , , , on April 10, 2015 by xi'an

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the new museum ruining my views!

Posted in pictures, Travel, University life with tags , , , , , , , , , , on November 8, 2014 by xi'an

lvmfarIn the past years, I have see a construction grow and grow under my office windows in Paris-Dauphine, ruining my views of the towers of La Défense, as seen on the above picture. This huge building designed by architect Frank Gehry has now opened as the Fondation Louis Vuitton museum, exposing artworks owned by LVMH and Bernard Arnault. Since I am very close to it and could not get an idea of what it looked like from my office, I took a Vélib yesterday and biked the kilometer between Porte Dauphine and the museum. As it had just opened, it was fairly crowded but I could still take a few pictures of this elegant sail-boat made of glass panels, without entering the art gallery itself…

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Once the novelty has worn out and the crowds thinned down, I will be back to look at the exhibits. In the meanwhile, I for sure will not forget its presence…!