SENSITIVITY INDICES FOR OUTPUT ON A RIEMANNIAN MANIFOLD

In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol' indices. One reason for the popularity of the Sobol' approach relies on the simplicity of the statistical estimation of these indices using the so-called pick and freeze method. In this work we propose and study sensitivity indices for the case where the output lies on a Riemannian manifold. These indices are based on a Cramer-von Mises like criterion that takes into account the geometry of the output support. We propose a pick and freeze like estimator of these indices based on an U-statistic. The asymptotic properties of these estimators are studied. Further, we provide and discuss some interesting numerical examples.