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 -th random variable for a quantity of interest (QoI) are computed by
(3.1.1)
(3.1.2)
See [Weirs12] for notation details. Note that, the second formulation looks slightly different from Eq. (9) of the original paper, becuase is switched with . This is to reuse in main index for computing the total index.
To reproduce the main and totol sensitivity indices of -th random variable, one can substitute with the simulation number specified in the user interface, with the vector of first QoI sample values (sample id from to ), with that of subsequent QoI samples (sample id from to ), and with that of sample id from to .
- Weirs12(1,2,3)
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