  We show how to apply Sobol's method of global sensitivity analysis to measure
the influence exerted by a set of nodes' evidence on a quantity of interest
expressed by a Bayesian network. Our method exploits the network structure so
as to transform the problem of Sobol index estimation into that of
marginalization inference. This way, we can efficiently compute indices for
networks where brute-force or Monte Carlo based estimators for variance-based
sensitivity analysis would require millions of costly samples. Moreover, our
method gives exact results when exact inference is used, and also supports the
case of correlated inputs. The proposed algorithm is inspired by the field of
tensor networks, and generalizes earlier tensor sensitivity techniques from the
acyclic to the cyclic case. We demonstrate the method on three medium to large
Bayesian networks that cover the areas of project risk management and
reliability engineering.
