Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Activates global sensitivity analysis based on decomposition of response variance into main, interaction, and total effects
Alias: none
Argument(s): none
Default: no variancebased decomposition
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  interaction_order  Specify the maximum number of variables allowed in an interaction when reporting interaction metrics.  
Optional  drop_tolerance  Suppresses output of sensitivity indices with values lower than this tolerance 
Dakota can calculate sensitivity indices through variancebased decomposition using the keyword variance_based_decomp
. This approach decomposes main, interaction, and total effects in order to identify the most important variables and combinations of variables in contributing to the variance of output quantities of interest.
Default Behavior
Because of processing overhead and output volume, variance_based_decomp
is inactive by default, unless required for dimensionadaptive refinement using Sobol' indices.
Expected Outputs
When variance_based_decomp
is specified, sensitivity indices for main effects, total effects, and any interaction effects will be reported. Each of these effects represents the percent contribution to the variance in the model response, where main effects include the aggregated set of univariate terms for each individual variable, interaction effects represent the set of mixed terms (the complement of the univariate set), and total effects represent the complete set of terms (univariate and mixed) that contain each individual variable. The aggregated set of main and interaction sensitivity indices will sum to one, whereas the sum of total effects sensitivity indices will be greater than one due to redundant counting of mixed terms.
Usage Tips
An important consideration is that the number of possible interaction terms grows exponentially with dimension and expansion order. To mitigate this, both in terms of compute time and output volume, possible interaction effects are suppressed whenever no contributions are present due to the particular form of an expansion. In addition, the interaction_order
and drop_tolerance
controls can further limit the computational and output requirements.
method, polynomial_chaos # or stoch_collocation sparse_grid_level = 3 variance_based_decomp interaction_order = 2
In this context, we take sensitivity analysis to be global, not local as when calculating derivatives of output variables with respect to input variables. Our definition is similar to that of[73] : "The study of how uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input."
Variance based decomposition is a way of using sets of samples to understand how the variance of the output behaves, with respect to each input variable. A larger value of the sensitivity index, , means that the uncertainty in the input variable i has a larger effect on the variance of the output. More details on the calculations and interpretation of the sensitivity indices can be found in[87].