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Given the following bayesian network:

enter image description here

Now I have to verify if $P(A, I) = P(A) * P(I)$ holds in this network. I know that $P(A, I) = P(A | I) * P(I)$ and I also know that $P(A|I) = P(A)$ if A and I are independent. But this does only hold when A and I are absolute independent. Bayesian networks model the conditional independence between different variables, but how can I check the absolute independence as in this case in such a network? I'm quite confused on how this conditional independence and absolute independence relate to each other?

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You just need to understand "d-separation" here. It's not so difficult:

http://classes.engr.oregonstate.edu/eecs/winter2015/cs536/slides/bayesnets3.4pp.pdf

http://www.andrew.cmu.edu/user/scheines/tutor/d-sep.html

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