Journal
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
Volume 8, Issue 6, Pages 483-493Publisher
BEGELL HOUSE INC
DOI: 10.1615/Int.J.UncertaintyQuantification.2018026498
Keywords
global sensitivity analysis; Sobol' indices; dependent variables
Funding
- National Science Foundation [DMS-1522765, DMS-1638521]
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The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and utility is more challenging with statistically dependent variables. This article develops an approximation theoretic perspective to interpret Sobol' indices in the presence of variable dependencies. The value of this perspective is demonstrated in the context of dimension reduction, a common application of the Sobol' indices. Theoretical analysis and illustrative examples are provided.
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