3.1. Global Sensitivity Analysis (Dakota)

Global Sensitivity Analysis in Dakota Engine is based on Eqs. (8) and (9) of [Weirs12]. Using the raw analysis samples shown in “RES” tab - “Data Values” tab after running a sensitivity analysis, one can reproduce the sensitivity indices as follows.

According to [Weirs12], the main and total Sobol indices of i-th random variable for a quantity of interest (QoI) are computed by

(3.1.1)Si=1nj=1nf(A)j(f(BA(i))jf(B)j)12nj=12nf(C)jf(C)j<f(C)>2
(3.1.2)SiT=12nj=1n(f(B)jf(BA(i))j)212nj=12nf(C)jf(C)j<f(C)>2

See [Weirs12] for notation details. Note that, the second formulation looks slightly different from Eq. (9) of the original paper, becuase A is switched with B. This is to reuse f(BA(i)) in main index for computing the total index.

To reproduce the main and totol sensitivity indices of i-th random variable, one can substitute n with the simulation number specified in the user interface, f(A) with the vector of first n QoI sample values (sample id from 1 to n), f(B) with that of subsequent n QoI samples (sample id from n+1 to 2n), and f(BA(i)) with that of sample id from (i+1)n+1 to (i+2)n.

Weirs12(1,2,3)
    1. Weirs, J. R. Kamm, L. P. Swiler, M. Ratto, S. Tarantola, B. M. Adams, W. J. Rider, and M. S Eldred. Sensitivity analysis techniques applied to a system of hyperbolic conservation laws. Reliability Engineering and System Safety, 107:157–170, 2012