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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),

OR

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?

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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