Constrained Global Sensitivity Analysis: Sobol’ indices for problems in non-rectangular domains

The variance-based method of global sensitivity analysis based on Sobol' sensitivity indices has become very popular among practitioners due to its ease of interpretation. 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. MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol’ sensitivity indices. Random Sampling - High Dimensional Model Representation metamodeling method is used to approximate models and constraints which significantly reduces the cost of evaluating Sobol’ sensitivity indices. Several model test functions with constraints are considered. The method is shown to be general and efficient