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Global sensitivity metrics from active subspaces


  • Constantine, Paul G.
  • Diaz, Paul


Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' total sensitivity indices and derivative-based global sensitivity measures. Active subspaces are part of an emerging set of tools for identifying important directions in a model's input parameter space; these directions can be exploited to reduce the model's dimension enabling otherwise infeasible parameter studies. In this paper, we develop global sensitivity metrics called activity scores from the active subspace, which yield insight into the important model parameters. We mathematically relate the activity scores to established sensitivity metrics, and we discuss computational methods to estimate the activity scores. We show two numerical examples with algebraic functions taken from simplified engineering models. For each model, we analyze the active subspace and discuss how to exploit the low-dimensional structure. We then show that input rankings produced by the activity scores are consistent with rankings produced by the standard metrics.

Suggested Citation

  • Constantine, Paul G. & Diaz, Paul, 2017. "Global sensitivity metrics from active subspaces," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 1-13.
  • Handle: RePEc:eee:reensy:v:162:y:2017:i:c:p:1-13
    DOI: 10.1016/j.ress.2017.01.013

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    References listed on IDEAS

    1. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
    2. Weirs, V. Gregory & Kamm, James R. & Swiler, Laura P. & Tarantola, Stefano & Ratto, Marco & Adams, Brian M. & Rider, William J. & Eldred, Michael S., 2012. "Sensitivity analysis techniques applied to a system of hyperbolic conservation laws," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 157-170.
    3. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    4. Crestaux, Thierry & Le Maıˆtre, Olivier & Martinez, Jean-Marc, 2009. "Polynomial chaos expansion for sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1161-1172.
    5. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    6. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
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    Cited by:

    1. Diaz, Paul & Constantine, Paul & Kalmbach, Kelsey & Jones, Eric & Pankavich, Stephen, 2018. "A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 141-155.


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