Archive for La Défense

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

Journée algorithmes stochastiques

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on September 27, 2017 by xi'an

On December 1, 2017, we will hold a day workshop on stochastic algorithms at Université Paris-Dauphine, with the following speakers

 Details and abstracts of the talks are available on the workshop webpage. Attendance is free, but registration is requested towards planning the morning and afternoon coffee breaks. Looking forward seeing ‘Og’s readers there, at least those in the vicinity!

And while I am targetting Parisians, crypto-Bayesians, and nearly-Parisians, there is another day workshop on Bayesian and PAC-Bayesian methods on November 16, at Université Pierre et Marie Curie (campus Jussieu), with invited speakers

and a similar request for (free) registration.

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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