Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables gives always the same output value). This paper proposes a global sensitivity analysis methodology for stochastic computer code (having a variability induced by some uncontrollable variables). The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, non parametric joint models (based on Generalized Additive Models and Gaussian processes) are discussed. The relevance of these new models is analyzed in terms of the obtained variance-based sensitivity indices with two case studies. Results show that the joint modeling approach leads accurate sensitivity index estimations even when clear heteroscedasticity is present.

💡 Research Summary

The paper addresses a notable gap in the field of global sensitivity analysis (GSA): existing variance‑based GSA techniques are designed for deterministic computer models, where a fixed set of inputs always yields the same output. In many scientific and engineering applications, however, computer codes are stochastic: they contain uncontrollable random elements (e.g., Monte‑Carlo sampling, turbulence models, random seed) that cause the output to vary even when the controllable inputs are held constant. This intrinsic randomness manifests as heteroscedasticity—output variance that depends on the input configuration. Ignoring this component leads to incomplete or biased sensitivity measures, because traditional Sobol indices only capture the contribution of inputs to the variance of the mean response.

To overcome this limitation, the authors propose a joint metamodeling framework that simultaneously models the conditional mean μ(x) = E