Efficient computation of Sobol' indices for stochastic models

TL;DR

This paper introduces an efficient global sensitivity analysis method for stochastic models, combining generalized Sobol' indices and surrogate models to identify influential parameters despite inherent randomness.

Contribution

It presents a novel approach to compute Sobol' indices for stochastic models using variance analysis and surrogate models, improving efficiency and applicability.

Findings

Successfully computed first order Sobol' indices for two stochastic models.

Demonstrated the method's efficiency and effectiveness in sensitivity analysis.

Showed how to analyze the statistical properties of the indices.

Abstract

Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying phenomena. We present a new global sensitivity analysis approach for stochastic models, i.e., models with both uncertain parameters and intrinsic stochasticity. Our method relies on an analysis of variance through a generalization of Sobol' indices and on the use of surrogate models. We show how to efficiently compute the statistical properties of the resulting indices and illustrate the effectiveness of our approach by computing first order Sobol' indices for two stochastic models.