Global Sensitivity Analysis • uqsa

library(uqsa)

With UQSA you can perform global sensitivity analysis (GSA) to find out how the uncertainty of the model output depend on the uncertainty in the parameter estimates.

UQSA computes first order and total order Sobol sensitivity index \(S_i\) and \(S_{iT}\) for independent parameter distributions using the method developed by Saltelli, 2002 with help from Halnes et al, 2009 .

We have also implemented a method based on binning to calculate first order sensitivities \(S_i\) also for non-independent distributions. This method can be applied directly on the distribution retrieved from an uncertainty quantification process.

In this example both methods for GSA are used and compared.

The Saltelli method requires that the parameter-matrices \(M1,M2\) and \(N\) is created. This can be done with the function saltelli_prior(). Next the corresponding model output has to be calculated (simulated). This gives corresponding matrices \(FM1,FM2\) and \(FN\). From \(FM1,FM2\) and \(FN\) the sobol indexes can next be calculated by the function gsa_saltelli(). For details see this example.

The binning method can be used directly on a (in most cases non-independent) sample from an uncertainty quantification process. The function gsa_binning()takes the parameter and output sample as input and returns Sobols first order sensitivity indexes. For details see this example.