GLOBAL SENSITIVITY INDICES, ESTIMATORS AND TRADEOFF BETWEEN EXPLORATIONS AND REPETITIONS FOR SOME STOCHASTIC MODELS
Résumé
Sobol sensitivity indices assess how the output of a given mathematical model is
sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the
inputs , thus raising questions as how to do a sensitivity analysis in such models. Practitioners have
been using a method that exploits the availability of softwares for deterministic models. For each
input, the stochastic model is repeated and the outputs averaged. These averages are seen as if they
were the outputs of a deterministic model and as such can feed standard softwares. In the context
of limited computational resources, one must ensure that the number of repetitions of the stochastic
model multiplied by the number of explorations of the input space is less than a fixed threshold.
The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed
and the sensitivity indices corresponding to the above method are formally defined. A bound on
an error criterion that penalizes bad rankings of the inputs is minimized. Moreover, exploiting a
representation of stochastic models obtained from minimal distributional assumptions, another kind
of Sobol-like sensitivity index is considered. Estimators of both kinds are constructed and their
asymptotic properties studied. The theory is illustrated on numerical experiments.
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