  Global sensitivity analysis (GSA) of numerical simulators aims at studying
the global impact of the input uncertainties on the output. To perform the GSA,
statistical tools based on inputs/output dependence measures are commonly used.
We focus here on dependence measures based on reproducing kernel Hilbert
spaces: the Hilbert-Schmidt Independence Criterion denoted HSIC. Sometimes, the
probability distributions modeling the uncertainty of inputs may be themselves
uncertain and it is important to quantify the global impact of this uncertainty
on GSA results. We call it here the second-level global sensitivity analysis
(GSA2). However, GSA2, when performed with a double Monte Carlo loop, requires
a large number of model evaluations which is intractable with CPU time
expensive simulators. To cope with this limitation, we propose a new
statistical methodology based on a single Monte Carlo loop with a limited
calculation budget. Firstly, we build a unique sample of inputs from a well
chosen probability distribution and the associated code outputs are computed.
From this inputs/output sample, we perform GSA for various assumed probability
distributions of inputs by using weighted HSIC measures estimators. Statistical
properties of these weighted esti-mators are demonstrated. Finally, we define 2
nd-level HSIC-based measures between the probability distributions of inputs
and GSA results, which constitute GSA2 indices. The efficiency of our GSA2
methodology is illustrated on an analytical example, thereby comparing several
technical options. Finally, an application to a test case simulating a severe
accidental scenario on nuclear reactor is provided.
