Lieu : IHP, Amphi Hermite
14.00 : Elena Di Bernardino (CNAM)
Titre : On some level functionals for random fields
Résumé : We deal with a stationary isotropic random field X and we assume it is partially observed through some level functionals. We aim at providing a methodology for a test of Gaussianity based on this information. More precisely, the level functionals are given by the Euler characteristic of the excursion sets above a finite number of levels. On the one hand, we study the properties of these level functionals under the hypothesis that the random field X is Gaussian. In particular, we focus on the mapping that associates to any level u the expected Euler characteristic of the excursion set above level u. On the other hand, we study the same level functionals under alternative distributions of X, such as chi-square, harmonic oscillator and shot noise.
15.00 : Antoine Godichon (INSA Rouen)
Titre : Algorithmes stochastiques pour la statistique robuste en grande dimension
Résumé : La médiane géométrique est souvent utilisée en statistique du fait de sa robustesse. On s'intéresse donc à des estimateurs rapides de la médiane, qui consistent en des algorithmes de gradient stochastiques moyennés. On définit aussi un nouvel indicateur de dispersion robuste, appelé Matrice de Covariance Médiane, avant d'en donner des estimateurs récursifs. Cette matrice, sous certaines hypothèses, a les mêmes sous-espaces propres que la matrice de covariance, mais est moins sensible aux données atypiques, et est donc très intéressante pour l'Analyse en Composantes Principales Robuste. Travail joint avec Hervé Cardot et Peggy Cénac (Université de Bourgogne).
16.00 : Julien Stoehr (Université Paris-Dauphine)
Titre : Noisy Hamiltonian Monte Carlo for doubly-intractable distributions
Résumé : Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented state space with transitions based on a deterministic differential flow derived from Hamiltonian mechanics. In practice, the evolution of Hamiltonian systems cannot be solved analytically, requiring numerical integration schemes. Under numerical integration, the resulting approximate solution no longer preserves the measure of the target distribution, therefore an accept-reject step is used to correct the bias. For doubly-intractable distributions -- such as posterior distributions based on Gibbs random fields -- HMC suffers from some computational difficulties: computation of gradients in the differential flow and computation of the accept-reject proposals poses difficulty. In this paper, we study the behaviour of HMC when these quantities are replaced by Monte Carlo estimates.