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