Discrete Random Variable in PCE

Hi everybody :slight_smile:
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 :slight_smile:

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 !
Best regards