I'd like to know if there is in the literature a (computationally cheap) algorithm to generate uniformly distributed variables in high dimension for a volume other than a cube and without using rejection sampling?


  • $\begingroup$ Rejection sampling is the only general technique or doing this AFAIK. $\endgroup$ – Alex C Mar 21 '19 at 12:31
  • $\begingroup$ @AlexC What about (linear) convex volumes? $\endgroup$ – Bob Jansen Mar 21 '19 at 14:07
  • $\begingroup$ @BobJansen by linear convex volumes, you mean volume delimited with at most 6 hyperplans? $\endgroup$ – stackoverflower Mar 21 '19 at 16:15
  • $\begingroup$ No, a volume delimited by an arbitrary number of hyperplanes. $\endgroup$ – Bob Jansen Mar 21 '19 at 16:33
  • $\begingroup$ In dimension 2, how would you do it for the set of point {(x,y) / x<=y, 0<=x<=1, 0<=y<=1} $\endgroup$ – stackoverflower Mar 22 '19 at 10:23

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