  In this paper, the sensitivity analysis of a single scale model is employed
in order to reduce the input dimensionality of the related multiscale model, in
this way, improving the efficiency of its uncertainty estimation. The approach
is illustrated with two examples: a reaction model and the standard
Ornstein-Uhlenbeck process. Additionally, a counterexample shows that an
uncertain input should not be excluded from uncertainty quantification without
estimating the response sensitivity to this parameter. In particular, an
analysis of the function defining the relation between single scale components
is required to understand whether single scale sensitivity analysis can be used
to reduce the dimensionality of the overall multiscale model input space.
