Laboratoire de Probabilités, Statistique et Modélisation
Présentation
Le Laboratoire de Probabilités, Statistique et Modélisation, dans sa forme actuelle, a résulté, au 1er janvier 1999, de la fusion de l'ancien Laboratoire de probabilité de l'université Paris 6 avec l'équipe de Probabilités et statistique de l'université Paris Diderot.
Le laboratoire compte environ 70 enseignants-chercheurs permanents, 50 thésards, une équipe administrative de 6 personnes. Il accueille de plus les activités de deux masters deuxième année, ce qui représente plus de 200 étudiants chaque année.
La thématique du laboratoire s'inscrit dans le domaine des mathématiques appliquées et a pour objet la modélisation, la description et l'estimation des phénomènes aléatoires. Les thèmes de recherche abordés ici concernent des domaines très variés et recouvrent aussi bien des mathématiques fondamentales que des applications dans des domaines aussi divers que la médecine, les sciences humaines, l'astrophysique, les assurances ou la finance...
Thèmes de recherche
1. Théorie ergodique et systèmes dynamiques
2. Modélisation stochastique
3. Mouvement brownien et calcul stochastique
4. Statistiques
Equipes de recherche
Le laboratoire comprend six équipes :
- Théorie ergodique et systèmes dynamiques,
- Modélisation stochastique,
- Mouvement brownien et calcul stochastique,
- Statistique,
- Probabilités numériques et mathématiques financières,
- Probabilités-statistiques-biologie.
[hal-01464530] New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality
Date: 3 Mayo 2018 - 17:53
Desc: We propose a new Borell-Brascamp-Lieb inequality which leads to novel sharp Euclidean inequalities such as Gagliardo-Nirenberg-Sobolev inequalities in R^n and in the half-space R^n_+. This gives a new bridge between the geometric pont of view of the Brunn-Minkowski inequality and the functional point of view of the Sobolev type inequalities. In this way we unify, simplify and generalize results by S. Bobkov-M. Ledoux, M. del Pino-J. Dolbeault and B. Nazaret.
[hal-01539752] Refine penetrance estimates in the main pathogenic variants of transthyretin hereditary (familial) amyloid polyneuropathy (TTR-FAP) using a new non-parametric approach (NPSE)
Date: 28 Mayo 2018 - 17:43
Desc: Significant variability of phenotype and age of onset are well known in TTR-FAP associated to a wide spectrum of pathogenic TTR variants, among which Val30Met is the most frequent [1,2]. Recently, new therapeutic options became available that should be administered from the very onset of symptoms. In this context, the knowledge of the risk of being symptomatic for mutation carriers (penetrance) is essential to adjust the follow-up of carriers and for patient management [3,4]. This study aims to refine penetrance estimates in the main pathogenic variants encountered in our TTR-FAP population using a newly developed non parametric approach named NPSE for Non-Parametric Survival Estimate.
[hal-00481055] Report card and indicators of quality in the Seine Estuary: from a scientific approach to an operational tool.
Date: 5 Mayo 2010 - 19:19
Desc: [...]
[hal-03796030] From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics
Date: 4 Oct 2022 - 12:51
Desc: We present a unifying, tractable approach for studying the spread of viruses causing complex diseases that require to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual's infection age, i.e., the time elapsed since infection, 1. The age distribution $n(t, a)$ of the population at time $t$ can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. 2. The frequency of type $i$ at time $t$ is simply obtained by integrating the probability $p(a, i)$ of being in state $i$ at age a against the age distribution $n(t, a)$. The advantage of this approach is three-fold. First, regardless of the number of types, macroscopic observables (e.g., incidence or prevalence of each type) only rely on a one-dimensional PDE "decorated" with types. This representation induces a simple methodology based on the McKendrick-von Foerster PDE with Poisson sampling to infer and forecast the epidemic. We illustrate this technique using a French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, here the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.
Autres contacts
U.F.R. Mathématiques
Sophie-Germain
75013 PARIS
