Statisfaction

Séminaire Parisien de statistique – October

Posted in Seminar/Conference by Julyan Arbel on 28 October 2010

Last  Monday I attended my first Séminaire Parisien de statistique this year. It takes place at Institut Henri Poincaré, whose famous Director is one of the 2010 Fields Medalists, Cédric Villani.

To quote Valencia discussant favorite adjectives, the three talks were terrific and thought-provoking.

Eric Moulines presented Multiple Try Methods in MCMC algorithms. Instead of a unique proposal at each step, one proposes several values, among which only one is kept. The proposals can be chosen independant, but introducing dependence in the right way speeds up the rate of convergence to the stationary distribution. An interesting feature of this algorithm, espacially for Pierre, is that it allows parallel computation (in multiple propositions) whereas the standard Metropolis-Hastings algorithm is essentially sequential. See as well Pierre, Christian and Murray Smith’s block Independent Metropolis-Hastings algorithm for further details.

Jean-Marc Bardet introduced a way to detect ruptures in time series. He focuses on causal time series, ie they can be written only in terms of present and past innovations, for example AR(\infty). A rupture at time t means the parameters change at t.

The must-see talk for me was Eric Barat presentation on BNP modeling for sapce-time emission tomography. For new comer, BNP means more than a bank: Bayesian nonparametric. It is nice to see a very efficient application of BNP methods to a medical field. Eric kindly gives his slides (cf below) which I recommend, espacially the section on random probability measures: he reviews properties of the Dirichlet process, various representations (Chinese restaurant, Stick-breaking), and extends to the Pitman-Yor process and Pitman-Yor mixture. Then he gives posterior simulations by Gibbs sampling. I am interested in dependent over time models, and I am thankful for Eric for his pointer to a recent article of Chung and Dunson on local Dirichlet process, a nifty and simple  construction of a Dependent Dirichlet process.

In a few days, I will try to make clear what the Dirichlet process is!

14 Responses

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  1. Arthur said, on 29 October 2010 at 04:14

    pas mal le coup de “BNP means more than a bank”… mais le slogan “plus qu’une banque” était plutôt attribué à une BP…. damned !
    sinon c’est quoi ce “Chinese restaurant process” ?

  2. Julyan said, on 29 October 2010 at 11:32

    Salut Arthur,
    Le Chinese restaurant process, c’est une définition du processus de Dirichlet d’un point de vue combinatoire. Si tu connais le principe d’urne de Polya, c’est la même chose avec une infinité de couleurs (pour le CRP, une infinité de tables ou de menus). Un beau dessin valant mieux qu’un long discours, je te renvoie aux slides d’Eric, qui a très bien dessiné les tables et les clients!

  3. Arthur said, on 29 October 2010 at 15:09

    En fait les slides d’Eric ne passent pas…
    ce sont des trucs genre Stepping Stone ? (http://tinyurl.com/23nrqf5)

    • Julyan said, on 29 October 2010 at 22:53

      J’ai corrigé le lien pour les slides. Avec l’urne de Polya (PU), on tire une couleur avec une probabilité proportionnelle au nombre de boules de la couleur (et on replace dans l’urne deux boules de cette couleur). Pour le CRP, le point commun avec la PU, c’est qu’un nouveau client s’assied à une table déjà occupée avec une probabilité proportionnelle au nombre de clients qui y sont attablés; le point nouveau, c’est qu’il peut choisir une nouvelle table, avec une probabilité proportionnelle à une constante fixée au départ. Comme le nombre de clients augmente, cette proba de choisir une nouvelle table diminue… on montre que le nombre de tables occupées croît comme le logarithme du nombre de clients.
      Du coup c’est lien au Stepping Stone. Bravo pour les animations!

  4. Jo said, on 5 November 2010 at 11:51

    salut
    impossible de downloader les slides. pb de serveur ?
    Jo

  5. […] — Julyan @ 11:24 Tags: bayesian nonparametrics, Dirichlet Process, stochastic process prior A promise is a promise, here is a post on the so-called Dirichlet process, or […]

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