I am trying to fit a PCE with 9 random variables, all uniformly distributed but one discretely uniformly distributed.
I have been doing some research, and it seems that what UQlab does is transform the discrete distribution into a continuous uniformly distribution. This could work, but it may lead to inaccurate results, right?
Furthermore, I am using this PCE to assess the Sobol sensitivity indices. Can I rely on these sensitivity analysis results from a PCE with 1 discrete random variable?
Thank you all in advance
Dear Gian Marco
Thanks for your question. So far there is no support for discrete variables in UQLab, but guess what : we’re working on it! The INPUT module is currently being enriched with such type of variables. This should appear in the next version.
Meanwhile you could address your problem as follows.
if your discrete variable has many possible outcomes, say 5-10 or more, you can definitely use a continuous uniform, and indeed round the outcomes to fit your real discrete realizations. It’s an approximation that should work.
if you have only 2 realizations of your discrete variable, say 0 or 1, you could fix it and compute Sobol’ indices conditioned on this value. And see if you observe the same patterns of sensitivity.
Hope this helps !