Geodesic
On derivative based global sensitivity criteria
Matematičeskoe modelirovanie, Tome 22 (2010) no. 12, pp. 137-143

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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. 
@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},
     publisher = {mathdoc},
     volume = {22},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_12_a9/}
}
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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/