Sobol' indices for problems defined in non-rectangular domains
  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. 
S. Kucherenko, O.V. Klymenko, N. Shah
math.ST math.NA stat.OT stat.TH