"Proving Variable Independence in a Network Using Markov Blanket"

[0rthodontist]

Is there a simple (meaning, memorable and not just a lot of crunching through probability formulas) proof that a variable is independent of the other variables in the network, given its Markov blanket?

 

[Sane]

Were you able to get this yet?

Is "a variable", node A in the Markov blanket? And "the other variables in the network" any node that does not belong to the blanket?

If so, then define independent?

 

[0rthodontist]

--No, I have not yet found this out

--A variable is a node in the Bayesian network, together with its conditional probability table

--"Independent" is used in the standard statistical sense

 

[Sane]

If you get it, let me know. I'd be interested to hear. I'm sure I'll realize it in due time, and get back to you if you don't to me first.