Hi Thomas,
The Gamma distribution in UQLab is parametrized by shape parameter k and scale parameter lambda (see uq_gamma_pdf.m), so with the corresponding formulas, you should obtain the correct moments – you can e.g. use UQLab’s function uq_gamma_PtoM to compute the moments of your Gamma distribution from given parameters. If that doesn’t give the right moments, could you upload your data set so that we can have a look whether there is indeed a bug?
Regarding full vs sparse PCE – normally it does not make sense to use OLS instead of sparse solvers like LARS. But indeed, if you have more than 6000 points in only three dimensions, this is more than enough to do OLS even with degree 20 or more.
Have you tried to check how well your fitted distributions describe your data? Other than that, reasons for the poor fit could be:
- the model is not smooth at all
- there is an additional source of randomness (noise), i.e., your model might return different values even when run twice with the same input parameters (see Xujia’s post on stochastic simulators)
Good luck with your research, let us know when (and how) you found a way to surrogate your model!