Part B.[4pt] Given your network above, which of the following (conditional) independences hold? Briefly justify your answer in each case:
- Independence of inferior-quality plutonium and low-quality heavy water in Springfield nuclear plant
Given no evidence at all, they are independent of each other.
- Independence of inferior-quality plutonium and low-quality heavy water in Springfield nuclear plant, given watery slurpees over at Apu's.
Using D-SEP, we can see that once SL is given, IP and LH are not independent (the "common-effect" case; since neither CM nor any of its descendants can be in the evidence for IP and LH to be independent)
- Independence of low-quality heavy-water and wateryness of slurpees at Apu's, given core-meltdown
Using D-Sep again, LH is indepedent of SL given CM (since the only path from LH to SL goes through CM, and it is an inter-causal path, and it gets blocked once CM is known). Another way of seeing this is that CM is the markov blanket of SL, and so given CM, SL is independent of everything else.