Estimating sensitivity indices based on Gaussian process metamodels with compactly supported correlation functions

Specific formulae are derived for quadrature-based estimators of global sensitivity indices when the unknown function can be modeled by a regression plus stationary Gaussian process using the Gaussian, Bohman, or cubic correlation functions. Estimation formulae are derived for the computation of process-based Bayesian and empirical Bayesian estimates of global sensitivity indices when the observed data are the function values corrupted by noise. It is shown how to restrict the parameter space for the compactly supported Bohman and cubic correlation functions so that (at least) a given proportion of the training data correlation entries are zero. This feature is important in the situation where the set of training data is large. The estimation methods are illustrated and compared via examples.