  Global sensitivity analysis aims at quantifying the impact of input
variability onto the variation of the response of a computational model. It has
been widely applied to deterministic simulators, for which a set of input
parameters has a unique corresponding output value. Stochastic simulators,
however, have intrinsic randomness due to their use of (pseudo)random numbers,
so they give different results when run twice with the same input parameters
but non-common random numbers. Due to this random nature, conventional Sobol'
indices, used in global sensitivity analysis, can be extended to stochastic
simulators in different ways. In this paper, we discuss three possible
extensions and focus on those that depend only on the statistical dependence
between input and output. This choice ignores the detailed data generating
process involving the internal randomness, and can thus be applied to a wider
class of problems. We propose to use the generalized lambda model to emulate
the response distribution of stochastic simulators. Such a surrogate can be
constructed without the need for replications. The proposed method is applied
to three examples including two case studies in finance and epidemiology. The
results confirm the convergence of the approach for estimating the sensitivity
indices even with the presence of strong heteroskedasticity and small
signal-to-noise ratio.
