Exercise 14.6

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

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

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

Figure [handedness-figure] Three possible structures for a Bayesian network describing genetic inheritance of handedness.