%0 Journal Article %A Fraiman, R. %A Gamboa, F. %A Moreno, Leonardo %D 2020 %I Begell House %K geodesic, pick and freeze method, Riemannian manifolds, sensitivity analysis, U-statistics %N 4 %P 297-314 %R 10.1615/Int.J.UncertaintyQuantification.2020029614 %T SENSITIVITY INDICES FOR OUTPUT ON A RIEMANNIAN MANIFOLD %U https://www.dl.begellhouse.com/journals/52034eb04b657aea,148a754a61aebe77,48ef5a0f3b45ff8e.html %V 10 %X 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. %8 2020-07-30