Asymptotic Analysis for the Variance-Based Global Sensitivity Indices

Table 1

Sensitivity indices and output uncertainty (both dimensionless) as calculated with the asymptotic formula and multidimensional quadrature.

Parameter	Asymptotic approximation	Sparse grid integration [15, 16]
Sensitivity index for {𝑋1,𝑋2,𝑋3,𝑋4}	0.3453	0.3453
Sensitivity index for 𝑋5,𝑋6	0.6126	0.6125
Sensitivity index for 𝑋7	0.0421	0.0421
Variance 𝐷	3.575⋅10^−5	3.567⋅10^−5
Standard deviation √𝐷	598 pcm	597 pcm