Séminaire de Probabilités et Statistique :

Le 07 avril 2025 à 13:45 - UM - Bât 09 - Salle de conférence (1er étage)

Présentée par Clarotto Lucia - Agro ParisTech

Spatio-temporal random fields on meshed surfaces defined from advection-diffusion SPDEs: application to environmental data

The aim of this work is to propose a statistical model for spatio-temporal data on meshed surfaces based on the Stochastic Partial Differential Equation (SPDE) modeling approach (Lindgren et al., 2011). Specifically, we focus on a class of advection-diffusion SPDEs defined on Euclidean surfaces or on smooth compact orientable closed Riemannian manifolds of dimension 2, and their discretization via a Galerkin approach (Clarotto et al., 2024). We demonstrate how this method enables the development of scalable algorithms for the simulation, inference and prediction of complex Gaussian random fields that are solutions to the discretized SPDE. The method is applied to simulated spatio-temporal datasets exhibiting advective and diffusive behavior, as well as to a real case study on solar radiation.

Clarotto, L., Allard, D., Romary, T., and Desassis, N. (2024). The SPDE approach for spatio-temporal datasets with advection and diffusion. Spatial Statistics, 62:100847. Lindgren, F., Rue, H., and Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov Random Fields: the Stochastic Partial Differential Equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(4):423–498.

Séminaire en salle 109, également retransmis sur zoom : https://umontpellier-fr.zoom.us/j/7156708132