Convex concentration inequalities and forward-backward stochastic calculus.
Risk bounds for new M-estimation problems
In this paper, we consider a new framework where two types of data are available: experimental data supposed to be i.i.d from and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon . We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data , reduced model complexity and computing...
Asymptotic normality and efficiency of two Sobol index estimators
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and...
Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model
Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called
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