Question: Suppose that in a Bayesian network containing an unobserved variable Y, all the variables in the Markov blanket MB(Y) have been observed. a. Prove that

Suppose that in a Bayesian network containing an unobserved variable Y, all the variables in the Markov blanket MB(Y) have been observed.

a. Prove that removing the node Y from the network will not affect the posterior distribution for any other unobserved variable in the network.

b. Discuss whether we can remove Y if we are planning to use (i) rejection sampling and (ii) likelihood weighting.

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