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H 1 Bayesian computation with INLA

Auteurs : Rue, Havard (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges. These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we present the first nonasymptotic risk bounds for maximum likelihood estimators (MLE) of the unknown distribution of the nodes. The proof relies on the construction of a graphical model encoding conditional dependencies that is extremely efficient to study n-regular graphs obtained using a round-robin scheduling. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. Following a classical construction in learning theory, the asymptotic likelihood is used to define a measure of performance for the MLE. Risk bounds for the MLE are finally obtained by subgaussian deviation results derived from concentration inequalities for Markov chains applied to our graphical model.

    Keywords : Bayesian computation; Integrated Nested Laplace Approximation (INLA); graphs model; maximum likelihood estimators (MLE)

    Codes MSC :
    62C10 - Bayesian problems; characterization of Bayes procedures
    62F15 - Bayesian inference
    65C40 - Computational Markov chains (numerical analysis)
    65C60 - Computational problems in statistics

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 01/11/2018
      Date de captation : 24/10/2018
      Collection : Research School
      Format : MP4
      Durée : 01:46:08
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants ; Etudiants Science Cycle 2
      Download : https://videos.cirm-math.fr/2018-10-24_Rue.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet chair: Masterclass in Bayesian statistics / Chaire Jean-Morlet : École de statistique bayésienne
    Organisateurs de la rencontre : Chopin, Nicolas ; Mengersen, Kerrie ; Pommeret, Denys ; Pudlo, Pierre ; Robert, Christian P. ; Ryder, Robin
    Dates : 22/10/2018 - 26/10/2018
    Année de la rencontre : 2018
    URL Congrès : https://www.chairejeanmorlet.com/2018-2-...

    Citation Data

    DOI : 10.24350/CIRM.V.19468403
    Cite this video as: Rue, Havard (2018). Bayesian computation with INLA. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19468403
    URI : http://dx.doi.org/10.24350/CIRM.V.19468403

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