A tradeoff between explorations and repetitions for estimators of two global sensitivity indices in stochastic models induced by probability measures
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 those 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 are
averaged. These averages are seen as if they came from a
deterministic model and hence Sobol's method can be used. However,
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. A bound on an error
criterion that penalizes bad rankings of the inputs' sensitivities
is minimized. The estimator induced by the empirical
method described above is shown to be asymptotically biased if the
number of repetitions goes to infinity too slowly. A
functional relationship between the output, the input and some
random noise is derived from minimal distributional assumptions,
which leads to a new sensitivity index with better statistical
properties. The theory is illustrated on numerical experiments.
Origine : Fichiers produits par l'(les) auteur(s)