A Central Limit Theorem for non identically distributed random variables with an application to Sobol indices

par Jérémy Boyer (IMT)

jeudi 28 mai 2026, 14:00 → 16:00 Europe/Paris

Johnson (1R3 - 1st floor)

The Central Limit Theorem (CLT) is one of the most well-known results in probability theory. It is traditionally stated for independent and identically distributed random variables. In this talk, I will present a version of the Central Limit Theorem where we only keep the independence assumption.

This generalization allows us to handle heterogeneous frameworks in statistics. I will then establish a connection between this version of the CLT and a classical estimator used in sensitivity analysis. To this end, I will introduce Sobol theory from the beginning, including Sobol indices and their interpretations, up to the main estimators used in practice. I will conclude my presentation by briefly explaining how the CLT introduced at the beginning can be used to prove the convergence of a particular estimator.