# Determining Independence in Bayesian Network

Consider the Bayesian Network Structure Below, decide whether the statements are true or false.

b) $$G \perp \!\!\! \perp A$$ (G is independent of A)

c) $$E \perp \!\!\! \perp H | \{D,G\}$$ (E and H are conditionally independent given D and G).

d) $$E\perp \!\!\! \perp H | \{C,D,F\}$$ (E and H are conditionally independent given C,D and F).

b) For these problems I applied the d-separation algorithm as explained here http://web.mit.edu/jmn/www/6.034/d-separation.pdf Using this approach I found that G and A are indeed independent.

c) True (using d-separation).

d) Also true (d-separation).

Could anyone please verify/correct my answers? I feel like at least one of the problems $$b,c$$ or $$d$$ should be false.

d) is false. H and E are connected through G in the d-seperation method.

• Welcome to Math SE! Can you elaborate a bit more on your answer? Feb 3, 2021 at 20:40