A common rationale for global sensitivity measures and their estimation

Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straight-forward Monte Carlo estimation procedure has a double-loop form. Recently, a more efficient single-loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density and information value. In this work, we give a unified proof of single-loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.