I tried to apply Sobol 2002 and 2007 sensitivity analysis to a LSM to evaluate for the different parameters the first order and total sobol index respectively Si and ST. But I always find non significant results (eg: ST=0.000000009 and Si= 0.999999222 for all the parameters). For the beginning I thought it was a problem of Monte Carlo dimentionality problem so I tried to make the same experiment but with a huge ensemble size (N= 600000 for only 2 parameters). I found the same results. I'm sure that my codecs are correct because when I use the Ishigami and the sobol benchmark I obtain significant results (e.g., in the attached paper link in the page 11). Could any one help me to understand this problem? Thanks in advance for all you answers and comments.
http://math.univ-lille1.fr/~jacques/Download/Publi/Intro-SA.pdf
This is very strange. Did you write this correctly? ST=0.000000009 and Si= 0.999999222 or is it inversely Si=0.000000009 and ST= 0.999999222?
The First-Order Sensitivity Index S_i can be assessed according to the paper:
Sobol, I, (1993).
“Sensitivity estimates for nonlinear mathematical models.”
Mathematical Modeling and Computational Experiment, 1, 407-414.
and the total-effects sensitivity Index S_Ti can be computed according to the paper:
Homma, T. and Saltelli, A., (1996).
“Importance measures in global sensitivity analysis of nonlinear models.”
Reliability Engineering and System Safety, 52, 1-17.
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