We present an alternative approach for this problem that is based ontechniques borrowed from a posteriori error analysis for finiteelement methods. Our approach allows the efficient computation of thegradient of a quantity of interest with respect to parameters atsample points. This derivative information is used in turn to producean error estimate for the information, thus providing a basis for bothdeterministic and probabilistic adaptive sampling algorithms. Thedeterministic adaptive sampling method can be orders of magnitudefaster than Monte-Carlo sampling in case of a moderate number ofparameters. The gradient can also be used to compute usefulinformation that cannot be obtained easily from a Monte-Carlo sample.For example, the adaptive algorithm yields a natural dimensionalreduction in the parameter space where applicable.