Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels

TL;DR

This paper introduces a novel global sensitivity analysis method for stochastic computer models using joint metamodels, effectively capturing heteroscedasticity to improve sensitivity index estimation accuracy.

Contribution

It develops a joint modeling framework combining mean and dispersion for stochastic models, utilizing non-parametric models like GAMs and Gaussian processes, which is a new approach in this context.

Findings

Joint models provide accurate sensitivity indices in heteroscedastic settings.

The approach outperforms traditional methods in complex stochastic models.

Case studies validate the effectiveness of the proposed methodology.

Abstract

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.