MATH-AmSud project FANTASTIC

statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations

Key words: parametrized stochastic differential equations, autoregressive processes, sensitivity analysis, Non- parametric functional regression, particle systems with mean field interactions, random sampling.

Project goals: the general aim of our research project is to tackle probabilistic and statistical issues driven by applications. It is divided in four independent axes.

Goal 1: The development of sensitivity analysis tools for parametrized stochastic differential equations, with an application to models arising in neurosciences.
Goal 2: The study of the emergence of collective behaviors in particle systems with mean field interaction.
Goal 3: Non-parametric regression estimation with Poisson and Wiener covariates.
Goal 4: Estimation of autoregressive random processes with random sampling times.

To handle these four axes, new developments are required both from the probability and statistical points of view.

Abstract: The general aim of our research project is to tackle probabilistic and statistical issues driven by applications. It is divided in four axes. The first one deals with sensitivity analysis for parametrized stochastic differential equations (SDE), with an application to models arising in neurosciences. The aim is to rank uncertain parameters with respect to their influence on the variability of a quantity of interest, related to the solution of the SDE. The second one is concerned with the emergence of collective behaviors in particle systems with mean field interaction. The aim for this second axis is to enlarge the class of stochastic models with collective organization features for which a mathematical analysis is possible. The two last axes are more focused to statistical issues, namely non-parametric regression estimation with Poisson and Wiener covariates and the estimation of autoregressive random processes with random sampling times. Regression estimation with Poisson covariates arises e.g., in speech recording analysis. That axis will make use of concentration inequalities for suprema of integral functionals of Poisson processes, as far hypercontractivity properties. Concerning the last axis, it seems a natural issue to be studied, as deterministic sampling is not always a reasonable assumption. Specific random times have been treated in the literature. The aim on this axis is to handle more general classes of random designs.

International Project Coordinator

Clémentine Prieur, Université Grenoble Alpes / Inria Grenoble Rhône-Alpes

Scientific coordinators at each institution

Karine Bertin, Universidad de Valparíso
Jose R. León, Universidad de la República
Clémentine Prieur, Université Grenoble Alpes / Inria Grenoble Rhône-Alpes

Members

Universidad de Valparaíso

Karine Bertin (senior)
Lisandro Fermin (senior)
Hector Olivero (senior)
Soledad Torres (senior)
Hector Araya (senior)
Tania Roa (junior)

Universidad de la República

Jose R. León (senior)
Federico Dalmao (senior)
Ernesto Mordecki (senior)

Université Grenoble Alpes / Inria Grenoble Rhône-Alpes

Clémentine Prieur (senior)
Pierre Etoré (senior)
Adeline Samson (senior)
Arthur Macherey (junior)
Anna Melnykova (junior)

Université Toulouse 3

Patrick Cattiaux (senior)

Inria Sophia Antipolis

Mireille Bossy (senior)

ENSIIE, LaMME

Sergio Pulido (senior)

Université Rennes 2

Nicolas Kluchnikoff (senior)

Conferences

Soledad Torres. Mesa de Trabajo Interdisciplinar Ð Modelos Predictivos covid 19 : SIR-X. 05/2020.
Tania Roa. 1er Workshop (virtual) de Estad’stica: Contribuciones de Posgrado. On consistency of least squares estimator in models sampled at random times driven by long memory noise. 08/2020.
Clémentine Prieur. Numerical Analysis of Stochastic Partial Differential Equations (NASPDE) 2020, 05-06/11/2020 (reported 04-05/11/2021), Luminy (France). Goal-oriented error estimation for the reduced basis method, application to sensitivity analysis. link
Clémentine Prieur. 02/2021. UQSay online
Karine Bertin. 04/2021. Congreso Zona sur. Estimación adaptativa en modelos de regresión funcional asociado a proceso de Wiener.
Karine Bertin. 09/2021. CLAM 2021, Uruguay. Charla: Adaptive regression with Brownian path covariate
Pierre Etoré. 04/2022. SIAM UQ Atlanta Global sensitivity analysis of models described by hypoelliptic systems of sotchastic differential equations.

Publications

H. Araya, N. Bahamonde, L. Fermin, T. Roa and S. Torres (2023). On the consistency of the least squares estimator in models sampled at random times driven by long memory noise: the renewal case, Statistica Sinica, Vol 33, n 1, DOI:10.5705/ss.202020.0457 link
K. Bertin, C. Genest, N. Klutchnikoff, and F. Ouimet, Minimax properties of Dirichlet kernel estimators. Submitted, 2021. arXiv
P. Etoré, J. R. León and C. Prieur (2021), A probabilistic point of view for the exact or approximated computation of the solution to Kolmogorov hypoelliptic equations. Submitted, 2021. arXiv
M. Billaud-Friess, A. Macherey, A. Nouy and C. Prieur (2022), A PAC algorithm in relative precision for bandit problem with costly sampling
To appear in Mathematical Methods of Operations Research arXiv
K. Bertin, N. Klutchnikoff, J. León and C. Prieur, Adaptive density estimation on bounded domains under mixing conditions, Electronic Journal of Statistics 14 (1), 2020. hal
K. Bertin, N. Klutchnikoff, F. Panloup and M. Varvenne, Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion, Statistical Inference for Stochastic Processes 23, 2020:271-300. link
K. Bertin and N. Klutchnikoff, Adaptive regression with Brownian path covariate, Annales de l'institut Henri Poincaré: Probabilités et Statistiques, 57, 1495-1520, 2021. arXiv
T. Roa, S. Torres. and C. Tudor. Limit distribution of the least square estimator with observations sampled at random times driven by standard Brownian motion. Communications in Statistics-Theory and Methods, 1-21. 2021. arXiv