  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 consider generalized chaos expansions built on
general tensor Hilbert basis. In this frame, we revisit the computation of the
Sobol' indices and give general lower bounds for these indices. The case of the
eigenfunctions system associated with a Poincar{\'e} differential operator
leads to lower bounds involving the derivatives of the analyzed function and
provides an efficient tool for variable screening. These lower bounds are put
in action both on toy and real life models demonstrating their accuracy.
