Numerical Algorithms For Evaluating Sobol

Sensitivity Analysis of Model Output: numerical algorithms for evaluating Sobol’ sensitivity indices
Rayna Georgieva
rayna@parallel.bas.bg (in collaboration with Sofiya Ivanovska)

IPP - BulgarianAcademy of Sciences, Sofia, Bulgaria
NATO Grant PDD(TC)-(ESP.EAP.CLG 982641) ”Monte Carlo Sensitivity Studies of Environmental Security”, The University of Reading, March 22, 2007

Outline
•Introduction • Formulation of the problem • Methods for evaluating global sensitivity indices • Sobol’ approach for evaluating global sensitivity indices • Numerical algorithms for multidimensionalintegration • Numerical experiments • Conclusion

NATO Grant PDD(TC)-(ESP.EAP.CLG 982641) ”MC Sensitivity Studies of Environmental Security”, The University of Reading, 03/22/2007 - p. 2/22

Motivation”The real voyage of discovery consists not in seeking new landscapes but in having new eyes.” (Marcel Proust)

Mathematical modelling is the use of mathematics to describe real-world phenomena: •investigate important questions about the observed world • explain real-world phenomena • test ideas • make predictions about the real world
NATO Grant PDD(TC)-(ESP.EAP.CLG 982641) ”MC SensitivityStudies of Environmental Security”, The University of Reading, 03/22/2007 - p. 3/22

Motivation

Jack Hardisty. ”Numerical experiments on the orthogonal profile with particular reference to changingenvironmental parameters.” Landscape Sensitivity, pp. 177–185, 1993.

”An appreciation of the stability, or otherwise, of an environmental system is achieved through the use of sensitivityanalysis. This approach generally recognises that the mathematical representation of the system will respond to either changes in the input parameters (parameter sensitivity) or to changes in therepresentation of the internal transfer functions (process sensitivity).”

NATO Grant PDD(TC)-(ESP.EAP.CLG 982641) ”MC Sensitivity Studies of Environmental Security”, The University of Reading, 03/22/2007 -...