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math.ST2025
Non-asymptotic confidence regions on RKHS. The Paley-Wiener and standard Sobolev space cases
Fabrice Gamboa, Olivier Roustant
We consider the problem of constructing a global, probabilistic, and non-asymptotic confidence region for an unknown function observed on a random design. The unknown function is a…
math.ST2019
Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices
O Roustant, F. Gamboa, B Iooss
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol' sensitivity indices. In this paper, we consid…