Hi Lenin,
Comparisons are always possible in some regard, although you need to clarify your question a bit.
FAST is a way to estimate first-order sensitivity indices using a spectral method. So-called "E-FAST" is an extension of the approach which estimates total-order sensitivity indices (Saltelli et al, 1999).
What I assume you mean by the Sobol' results is using the Monte Carlo procedure of Sobol e.g. Sobol (1993) to estimate first-order and possibly total-order sensitivity indices.
When you talk about comparing, I guess you mean that you have results from both on your model and want to understand the difference? Or a more general comparison?
I think it is fair to argue that these days, FAST is slightly outdated. The initial advantage was that it improves computation efficiency over Monte Carlo, but comes at the cost of extra assumptions of smoothness, and some bias (see e.g. Xu and Gertner, 2011). There are now more efficient approaches based on metamodels (aka surrogate models or emulators), such as Gaussian processes, or polynomial chaos expansions. A very nice package on these (and more info) can be found at http://www.uqlab.com/.
However, even metamodels impose assumptions. Arguably, if can run your model lots of times, you should opt for the Monte Carlo approach because it will always converge as long as your model is square-integrable (not a very restrictive assumption). You can monitor convergence by plotting the values of sensitivity indices as the number of model evaluations increases. When the estimates become acceptably stable (e.g. vary only 1% over a certain number of iterations), you can have fairly good confidence in your results.
Not sure if this answers your q, but if you clarify I could try to elaborate.
Best
William
Saltelli, A., Tarantola, S. and Chan, K. (1999), Quantitative model-independent method for global sensitivity analysis of model output, Technometrics 41(1), 39–56
Sobol’, I. M. (1993), Sensitivity estimates for nonlinear mathematical models, Mathematical Modeling and Computational Experiment 1(4), 407–414
Xu, C. and Gertner, G. (2011), Understanding and comparisons of different sampling approaches for the Fourier amplitudes sensitivity test (FAST), Computational Statistics and Data Analysis 55, 184–198
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