Consider a mathematical model $f(x)$ defined in the $n$-dimensional unit cube, $x=(x_1,\dots,x_n)$. How to estimate the global sensitivity of $f(x)$ with respect to $x_i$? If $f(x)\in L_2$, global sensitivity indeces provide practical answers to the question. Derivative based criteria are less reliable but sometimes easier for computing. In this note a new derivative based global sensitivity criterion is compared with the correspondding global sensitivity index. It is proved that in the special case when $f(x)$ is a linear function of $x_i$, the estimates are equal. However the Monte Carlo approximations to the derivative based criterion converge faster. Thus the derivative based criterion may be useful in situations when the dependence of $f(x)$ on $x_i$ is near to linear. It can also be applied for detecting nonessential variables $x_i$.
Keywords:
sensitivity analysis, mathematical model, method Monte Carlo, variance, global sensitivity indices.
I. M. Sobol. On derivative based global sensitivity criteria. Matematičeskoe modelirovanie, Tome 22 (2010) no. 12, pp. 137-143. http://geodesic.mathdoc.fr/item/MM_2010_22_12_a9/
@article{MM_2010_22_12_a9,
author = {I. M. Sobol},
title = {On derivative based global sensitivity criteria},
journal = {Matemati\v{c}eskoe modelirovanie},
pages = {137--143},
year = {2010},
volume = {22},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MM_2010_22_12_a9/}
}
TY - JOUR
AU - I. M. Sobol
TI - On derivative based global sensitivity criteria
JO - Matematičeskoe modelirovanie
PY - 2010
SP - 137
EP - 143
VL - 22
IS - 12
UR - http://geodesic.mathdoc.fr/item/MM_2010_22_12_a9/
LA - ru
ID - MM_2010_22_12_a9
ER -
%0 Journal Article
%A I. M. Sobol
%T On derivative based global sensitivity criteria
%J Matematičeskoe modelirovanie
%D 2010
%P 137-143
%V 22
%N 12
%U http://geodesic.mathdoc.fr/item/MM_2010_22_12_a9/
%G ru
%F MM_2010_22_12_a9
[2] I. M. Sobol', S. Kucherenko, “Derivative based global sensitivity measures and their link with global sensitivity indices”, Maths and Computers in Simulation, 79 (2009), 3009–3017 | DOI | MR | Zbl
[3] F. Campolongo, J. Caribon, A. Saltelli, “An effective screening design for sensitivity analysis of large models”, Environmental Modelling and Software, 22 (2007), 1509–1518 | DOI
[4] A. Kiparissides, S. S. Kucherenko, A. Mantalaris, E. N. Pistikopoulos, “Global Sensitivity Analysis challenges in biological systems modeling”, Industrial and Engineering Chemistry Research, 48 (2009), 7168 | DOI
