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This might be a very basic question, but it seems that in all the examples I've seen, the inverse sampling method (i.e., input uniform RV into the inverse of CDF of desired PDF/probability distribution), is usually done for 1D random variables.

This doesn't seem to be very easy for higher dimensional settings, i.e., random vectors.

Can someone who is knowledgeable in this area let me know whether:

  1. inverse sampling can be done for generating random vectors (that is, inverting a CDF of two or more variables). For instance, using the inverse of the CDF of the joint Gaussian probability density function.
  2. what is the method for generating random vectors. (what's wrong with doing 1D inverse sampling method for each component of the random vector?)

(Note: I don't know anything about sampling)

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  • $\begingroup$ what's wrong with doing 1D inverse sampling method for each component of the random vector? What if the margins are correlated or otherwise not independent? $\endgroup$ Commented May 3, 2024 at 18:08

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