Discussion
Why is the Markov blanket exactly what Gibbs sampling needs?
Answer: A
Since a variable is conditionally independent of the rest of the network given its blanket, the correct conditional distribution can be computed from local information alone, which is what makes each update cheap. Size, observation and ordering are different matters. A structural property that makes a global computation local is what turns an intractable algorithm into a practical one, and it is the reason the blanket is defined at all. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.
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