The Saltelli Sampling
Basics
The sensitivity analysis described by Saltelli (Saltelli, 2002) is a variance-based method and consists in determine the impact of parameters and/or variables on the variance of the output(s) of the model.
Two parameter sample matrices A and B of N lines corresponding to the N simulation runs and k columns corresponding to the k parameters and/or variables studied are generated with a LHS procedure (these random samplings occurred for each parameter in their intervals of values). And k matrices Ci , i = 1, …, k, where column i comes from matrix A and all the other k-1 columns come
from matrix B are built.
The model is then run on each row u of the k + 2 matrices to provide k + 2 vectors YA , YB and YCi
where Y represents the output of the model.
Then, first-order and total effect sensitivity indices for each parameters are calculated.
By definition, STi is greater than Si , or equal to Si in the case when the studied parameter is not involved in any interaction with other parameters. STi − Si is a measure of how much the studied parameter is involved in interaction with any other parameters. The greater STi − Si, the stronger is the interaction.
STi = 0 implies that the studied parameter is non influential and can be set anywhere in its distribution without affecting the variance of the outputs.
Creation
To create a Saltelli Sampling :
> Right click on the Sampling Composition area, select Add Sampling and then Saltelli in the Sampling panel that shows up.
> A configuration panel appears. Select the number of required Samples (for Double Prototypes)
> Click on create, and this Sampling is now ready to be embedd in an Exploration Task
Example
Let’s create a Saltelli Sampling on 2 Bounded Domains
> create first two Prototypes of type Double named p1 and p2. > then create two Bounded Domains respectively varying from 0 to 100 and from 0.1 to 0.9 (NB: a Bounded Domain is a Range Domain without step parameter).
> add a Saltelli Sampling on the Sampling Composition Area > associate the Prototype p1 to the first Domain and the Prototype p2 to the second one (NB: click on the ? on the connector) > connect both Domains to the Saltelli Sampling and the Saltelli Sampling to the final stone (Shift + drag from the source to the target)
> create an Exploration Task and select the previously built Sampling > add the Exploration Task on a Scene > add a Display Hook on it
> the Mole (of only one Task !) is now ready to be run : press the build Button
> the execution shows up in a new tab. Set the Hook to see the Prototypes p1 and p2. 
> Switch to the Execution progress view and press the play button 
> the Mole is run. A possible output (the Saltelli Simpling is a stocahstic algorithm) is two vectors (corresponding to the Saltelli settings): {p1=[0.15115618632460412, 0.15193883353270382, 0.19490695222641902, 0.154048539071156, 0.17424076489457221, 0.15491282352520036, 0.20697948755159942, 0.15596959981423936, 0.2082383791213953, 0.19908559532124612, 0.15491282352520036, 0.20697948755159942, 0.15596959981423936, 0.2082383791213953, 0.19908559532124612, 0.15115618632460412, 0.15193883353270382, 0.19490695222641902, 0.154048539071156, 0.17424076489457221],
p2=[1829.26876894635, 1207.264745365119, 1341.2953265300976, 1215.540779652557, 1475.850562837314, 1538.739858993352, 1495.704524051921, 1455.9386470507202, 1560.832881300063, 1159.6141161636124, 1829.26876894635, 1207.264745365119, 1341.2953265300976, 1215.540779652557, 1475.850562837314, 1538.739858993352, 1495.704524051921, 1455.9386470507202, 1560.832881300063, 1159.6141161636124]}