Institut de Mathématiques de Marseille, UMR 7373




Rechercher


Accueil >

9 octobre 2017: 3 événements

Séminaire

  • Séminaire Statistiques

    Lundi 9 octobre 14:00-15:00 - Estelle KUHN - INRA, Jouy-en-Josas

    Testing variance components in nonlinear mixed effects models

    Résumé : Joint work with Charlotte Baey and Paul-Henry Cournède (CentraleSupélec, MICS)
    Mixed effects models are widely used to describe inter and intra individual variabilities in a population. A fundamental question when adjusting such a model to the population consists in identifying the parameters carrying the different types of variabilities, i.e. those that can be considered constant in the population, referred to as fixed effects, and those that vary among individuals, referred to as random effects.
    In this work, we propose a test procedure based on the likelihood ratio one for testing if the variances of a subset of the random effects are equal to zero. The standard theoretical results on the asymptotic distribution of the likelihood ratio test can not be applied in our context. Indeed the assumptions required are not fulfilled since the tested parameter values are on the boundary of the parameter space. The issue of variance components testing has been addressed in the context of linear mixed effects models by several authors and in the particular case of testing the variance of one single random effect in nonlinear mixed effects models. We address the case of testing that the variances of a subset of the random effects are equal to zero. We proof that the asymptotic distribution of the test is a chi bar square distribution, indeed a mixture of chi square distributions, and identify the weights of the mixture. We highlight that the limit distribution depends on the presence or not of correlations between the random effects. We present numerical tools to compute the corresponding quantiles. Finally, we illustrate the finite sample size properties of the test procedure through simulation studies and on real data.

    JPEG - 33.1 ko
    Estelle KUHN

    Lieu : FRUMAM, salle de séminaire du 2ème étage - Aix-Marseille Université - Site St Charles
    3, place Victor Hugo - case 39
    13331 MARSEILLE Cedex 03

    Exporter cet événement
    Document(s) associé(s) :

    En savoir plus : Séminaire Statistiques

  • Séminaire Géométrie, Dynamique et Topologie (GDT)

    Lundi 9 octobre 14:00-15:00 - Yoshinori HASHIMOTO - I2M, Marseille

    Geometric quantisation and extremal Kähler metrics

    Résumé : Existence of canonical Kähler metrics, such as Kähler-Einstein metrics or more generally extremal Kähler metrics, has been studied intensively in recent years. Although this amounts to solving a nonlinear PDE, it is known to have a deep connection to a purely algebro-geometric notion called K-stability, defined in terms of Geometric Invariant Theory. In the first part of this talk, we shall review the background and introduce Donaldson’s approach to this problem with ideas from geometric quantisation. In presence of symmetries this approach does not naively work, and in the second part of the talk we shall introduce a new “quantising” equation to extend Donaldson’s result in presence of symmetries, and discuss its implications to relative K-stability.

    JPEG - 6.2 ko
    Yoshinori HASHIMOTO

    Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
    39 rue Frédéric Joliot-Curie
    13453 Marseille cedex 13

    Exporter cet événement
    Document(s) associé(s) :

    En savoir plus : Séminaire Géométrie, Dynamique et Topologie (GDT)

  • Séminaire Statistiques

    Lundi 9 octobre 15:30-16:30 - Gilles DIDIER - I2M, Marseille

    Likelihood of tree topologies with fossils and diversification rate estimation

    Résumé : Since the diversification process cannot be directly observed at the human scale, it has to be studied from the information available, namely the extant taxa and the fossil record. In this sense, phylogenetic trees including both extant taxa and fossils are the most complete representations of the diversification process that one can get. Such phylogenetic trees can be reconstructed from molecular and morphological data, to some extent. Among the temporal information of such phylogenetic trees, fossil ages are by far the most precisely known (divergence times are inferences calibrated mostly with fossils). We propose here a method to compute the likelihood of a phylogenetic tree with fossils in which the only known time information is the fossil ages, and apply it to the estimation of the diversification rates from such data. Since it is required in our computation, we provide a method for determining the probability of a tree topology under the standard diversification model.
    Testing our approach on simulated data shows that the maximum likelihood rate estimates from the phylogenetic tree topology and the fossil dates are almost as accurate as those obtained by taking into account all the data, including the divergence times. Moreover, they are substantially more accurate than the estimates obtained only from the exact divergence times (without taking into account the fossil record).
    We also provide an empirical example composed of 50 Permo-carboniferous eupelycosaur (early synapsid) taxa ranging in age from about 315 Ma (Late Carboniferous) to 270 Ma (shortly after the end of the Early Permian). Our analyses suggest a speciation (cladogenesis, or birth) rate of about 0.1 per lineage and per My, an extinction rate marginally lower, and a considerable hidden paleobiodiversity of early synapsids.

    JPEG - 20.1 ko
    Gilles DIDIER

    Lieu : FRUMAM, salle de séminaire du 2ème étage - Aix-Marseille Université - Site St Charles
    3, place Victor Hugo - case 39
    13331 MARSEILLE Cedex 03

    Exporter cet événement
    Document(s) associé(s) :

    En savoir plus : Séminaire Statistiques