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?