  A novel theoretical and numerical framework for the estimation of Sobol
sensitivity indices for models in which inputs are confined to a
non-rectangular domain (e.g., in presence of inequality constraints) is
developed. Two numerical methods, namely the quadrature integration method
which may be very efficient for problems of low and medium dimensionality and
the MC/QMC estimators based on the acceptance-rejection sampling method are
proposed for the numerical estimation of Sobol sensitivity indices. Several
model test functions with constraints are considered for which analytical
solutions for Sobol sensitivity indices were found. These solutions were used
as benchmarks for verifying numerical estimates. The method is shown to be
general and efficient.
