Stochastic models are used in many scientific fields, including mechanics, physics, life sciences, queues and social-network studies, chemistry. Stochastic modeling is necessary when deterministic evolutions cannot correctly represent the dynamics because of unresolved small-scale fluctuations or significant inherent noise. Stochastic models are usually not perfectly known and involve some parameters that should be considered uncertain. It is then critical to assess the uncertain parameters' impact on the model predictions. This assessment usually relies on sensitivity analyses (SA), which characterize changes in the model output when the uncertain parameters vary. For stochastic models, the SA classically focuses on the prediction's statistical moments and their (local) derivatives with the uncertain parameters.

This presentation introduces a global approach to SA in stochastic systems, relying on variance decomposition methods (ANOVA, Sobol indices). Compared to other methods, our SA is global, concerning both the parameters and stochasticity, owing to a decomposition of the variance into stochastic, parametric, and mixed contributions. 

This talk will detail two approaches depending on the nature of the stochastic models. First, I will focus on Stochastic Differential Equations (SDE) models involving uncertain parameters. In this case, one can exploit possible smooth dependencies on the parameters to perform spectral expansions through Galerkin or non-intrusive strategies. Second, we consider stochastic simulators governed by a set of reaction channels. In this case, we identify the individual reaction channel dynamics as an independent source of stochasticity and propose an approach to estimate their respective contribution to the variance. With this decomposition scheme, the case of uncertain rate parameters will be finally considered.