variance_based_decomp

Activates global sensitivity analysis based on decomposition of response variance into contributions from variables

Specification

• Alias: None

• Arguments: None

• Default: no variance-based decomposition

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		drop_tolerance	Suppresses output of sensitivity indices with values lower than this tolerance

Description

Dakota can calculate sensitivity indices through variance based decomposition using the keyword variance_based_decomp. These indicate how important the uncertainty in each input variable is in contributing to the output variance.

Default Behavior

Because of the computational cost, variance_based_decomp is turned off as a default.

If the user specified a number of samples, N, and a number of nondeterministic variables, M, variance-based decomposition requires the evaluation of N*(M+2) samples. Note that specifying this keyword will increase the number of function evaluations above the number requested with the ``samples`` keyword since replicated sets of sample values are evaluated.

Expected Outputs

When variance_based_decomp is specified, sensitivity indices for main effects and total effects will be reported. Main effects (roughly) represent the percent contribution of each individual variable to the variance in the model response. Total effects represent the percent contribution of each individual variable in combination with all other variables to the variance in the model response

Usage Tips

To obtain sensitivity indices that are reasonably accurate, we recommend that N, the number of samples, be at least one hundred and preferably several hundred or thousands.

Examples

method,
  sampling
    sample_type lhs
    samples = 100
    variance_based_decomp

Theory

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 [STCR04] : “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, \(S_i\) , 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 [STCR04] and [WKS+12].