Date/heure
15 février 2024
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Mike Pereira (Université Paris Sciences & Lettres)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
Many applications in spatial and spatio-temporal statistics require data to be modeled by Gaussian processes on non-Euclidean domains, or with non-stationary properties. Using such models generally comes at the price of a drastic increase in operational costs (computational and storage-wise), rendering them hard to apply to large datasets. In this talk, we propose a solution to this problem, which relies on the definition of a class of random fields on Riemannian manifolds. These fields extend ongoing work that has been done to leverage a characterization of the random fields classically used in Geostatistics as solutions of stochastic partial differential equations. The discretization of these generalized random fields, undertaken using a finite element approach, then provides an explicit characterization that is leveraged to solve the scalability problem. Indeed, matrix-free algorithms, in the sense that they do not require to build and store any covariance (or precision) matrix, are derived to tackle for instance the simulation of large Gaussian fields with given covariance properties, even in the non-stationary setting or on surfaces.