Before revision: Sparse polynomial chaos expansions ( PCEs ) are an efficient and widely used surrogate modeling method in uncertainty quantification  .
After revision: Sparse polynomial chaos expansions ( PCEs ) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in the most efficient way, several approaches for so-called basis-adaptive sparse PCE have been proposed to determine the set of polynomial regressors ("basis") for PCE adaptively .