UE Stochastic approaches for uncertainty quantification

Degrees incorporating this pedagocial element :


Uncertainty analysis aims to understand the impact of input variables or noise on these input variables on the code output variables. Usually, deterministic tools of differential calculus are used. For example, a basic index is obtained via the derivative of one output respective to one imput. Such approach remains local because derivatives are generally computed at specific points. In this deterministic approach, we are interested by the automatic differentiation tools which aim at efficiently compute complex code derivatives.

Evaluation :

Written exam E
Presentation of a research paper L


Basic knowledges in probability and statistics

Targeted skills

The stochastic approach of uncertainty analysis, on which this lecture focuses, aims at studying global criteria based on joint pdf modelisation of the problem variables. The obtained sensitivity indices describe the global variabilities of the phenomena. For example, the Sobol sensitivity index is given by the ratio between the ouput variance conditionally to one input and the total output variance. Computation of such quantities leads to very interesting statistical problems that we propose to study. For example, the efficient estimation of sensitivity indices from a few runs relates to semi or non-parametric estimation techniques. The stochastic modelisation of the input/output relation ship is another solution. We can look for models with specific properties (parcimonious representation using ad hoc response surfaces, having remarkable algebraic properties as orthogonality, etc).


Sensitivity analysis. Saltelli, Andrea and Chan, Karen and Scott, E Marian and others, vol. 1 (2000), Wiley New York

Analyse de sensibilité et exploration de modèles: application aux sciences de la nature et de l'environnement. Faivre, Robert and Iooss, Bertrand and Mahévas, Stéphanie and Makowski, David and Monod, Hervé (2013). Editions Quae.