Derivative-based integral equalities and inequality: A proxy-measure for sensitivity analysis

Matieyendou Lamboni

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 179, issue C, 137-161

Abstract: Weighted Poincaré-type and related inequalities provide upper bounds of the variance of functions. Their applications in sensitivity analysis allow for quickly identifying the active inputs. Although the efficiency in prioritizing inputs depends on those upper bounds, the latter can take higher values, and therefore useless in practice. In this paper, an optimal weighted Poincaré-type inequality and gradient-based expression of the variance (integral equality) are studied for a wide class of probability measures. For a function f:R→Rn with n∈N∗, we show that Varμf=∫Ω×Ω∇fx∇fx′TFmin(x,x′)−F(x)F(x′)ρ(x)ρ(x′)dμ(x)dμ(x′),and Varμf⪯12∫Ω∇fx∇fxTF(x)1−F(x)ρ(x)2dμ(x),with Varμf=∫ΩffTdμ−∫Ωfdμ∫ΩfTdμ, F and ρ the distribution and the density functions, respectively. Such results are generalized to cope with any function f:Rd→Rn using cross-partial derivatives. The new results allow for proposing a new proxy-measure for sensitivity analysis. Finally, analytical tests and numerical simulations show the relevance of our proxy-measure for identifying important inputs by improving the upper bounds from the Poincaré inequalities.

Keywords: Derivative-based ANOVA; Derivative global sensitivity measure; Generalized sensitivity indices; Optimal Poincaré’-type inequalities; Sobol’s indices (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475420302706
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:179:y:2021:i:c:p:137-161

DOI: 10.1016/j.matcom.2020.08.006

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
Bibliographic data for series maintained by Catherine Liu ().