1Blurb:: 2Activates global sensitivity analysis based on decomposition of 3response variance into contributions from variables 4 5Description:: 6Dakota can calculate sensitivity indices through variance based 7decomposition using the keyword \c variance_based_decomp. These 8indicate how important the uncertainty in each input variable is in 9contributing to the output variance. 10 11<b> Default Behavior </b> 12 13Because of the computational cost, \c variance_based_decomp is turned 14off as a default. 15 16If the user specified a number of samples, N, and a number of 17nondeterministic variables, M, variance-based decomposition requires 18the evaluation of N*(M+2) samples. <b> Note that specifying this 19keyword will increase the number of function evaluations above the 20number requested with the \c samples keyword since replicated sets of 21sample values are evaluated. </b> 22 23<b> Expected Outputs </b> 24 25When \c variance_based_decomp is specified, sensitivity indices for 26main effects and total effects will be reported. Main effects 27(roughly) represent the percent contribution of each individual 28variable to the variance in the model response. Total effects 29represent the percent contribution of each individual variable in 30combination with all other variables to the variance in the model 31response 32 33<b> Usage Tips </b> 34 35To obtain sensitivity indices that are reasonably accurate, we 36recommend that N, the number of samples, be at least one hundred and 37preferably several hundred or thousands. 38 39Topics:: 40Examples:: 41\verbatim 42method, 43 sampling 44 sample_type lhs 45 samples = 100 46 variance_based_decomp 47\endverbatim 48Theory:: 49In this context, we take sensitivity analysis to be global, not local 50as when calculating derivatives of output variables with respect to 51input variables. Our definition is similar to that of \cite Sal04 : 52"The study of how uncertainty in the output of a model can be 53apportioned to different sources of uncertainty in the model input." 54 55Variance based decomposition is a way of using sets of samples to 56understand how the variance of the output behaves, with respect to 57each input variable. A larger value of the sensitivity index, 58\f$S_i\f$, means that the uncertainty in the input variable i has a 59larger effect on the variance of the output. More details on the 60calculations and interpretation of the sensitivity indices can be 61found in \cite Sal04 and \cite Weirs10. 62 63Faq:: 64See_Also:: 65