I have a question about sampling. Suppose X1, X2 and X3 are observed and Y is not observed. How do you draw from the distribution that follows this constraint:

P(Y | X1, X2, X3) = P(Y | X1, X2)?

Here, X3 and X1 are independent, but not X3 and X2.

To put it differently, I observe 3 variables - X1, X2 and X3 in the form of vectors, where X1 and X3 are independent. There is another variable Y - unobserved - about which we know that it is conditionally independent of X3, given X1 and X2, i.e.

P(Y | X1, X2, X3) = P(Y | X1, X2),


P(Y, X3 | X1, X2) = P(Y | X1, X2) . P(X3 | X1, X2).

Is it possible to draw samples from the unknown distribution of Y?


closed as unclear what you're asking by Xi'an, kjetil b halvorsen, Peter Flom Jan 7 at 11:23

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  • $\begingroup$ Is X3 independent of X1 and X2? $\endgroup$ – user2974951 Jan 7 at 11:31
  • $\begingroup$ X3 is independent of X1, but not X2. $\endgroup$ – Ayush Chauhan Jan 8 at 13:35
  • $\begingroup$ AFAICT, you want the probability of Y given stuff, but have no data on Y. That can't be done. $\endgroup$ – gung Jan 8 at 14:44