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The so-called polynomial chaos expansion is widely used in computerexperiments. For example, it is a powerful tool to estimate Sobol' sensitivityindices. In this paper, we consider generalized chaos expansions built ongeneral tensor Hilbert basis. In this frame, we revisit the computation of theSobol' indices and give general lower bounds for these indices. The case of theeigenfunctions system associated with a Poincar{\'e} differential operatorleads to lower bounds involving the derivatives of the analyzed function andprovides an efficient tool for variable screening. These lower bounds are putin action both on toy and real life models demonstrating their accuracy.

Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices