 Derivative-based global sensitivity measures: General links with Sobol’ indices and numerical testsM. Lamboni, B. Iooss, A.-L. Popelin and F. Gamboa Mathematics and Computers in Simulation (MATCOM), 2013, vol. 87, issue C, 45-54 Abstract: The estimation of variance-based importance measures (called Sobol’ indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the derivative-based global sensitivity measures (DGSM), defined as the integral of the squared derivatives of the model output, showing that it can help to solve the problem of dimensionality in some cases. We provide a general inequality link between DGSM and total Sobol’ indices for input variables belonging to the class of Boltzmann probability measures, thus extending the previous results of Sobol and Kucherenko for uniform and normal measures. The special case of log-concave measures is also described. This link provides a DGSM-based maximal bound for the total Sobol indices. Numerical tests show the performance of the bound and its usefulness in practice. Keywords: Boltzmann measure; Global sensitivity analysis; Log-concave measure; Poincaré inequality; Sobol’ indices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:87:y:2013:i:c:p:45-54 DOI: 10.1016/j.matcom.2013.02.002 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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