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I have this joint probability distribution between the two binary values $A$ and $B$ $$ \begin{array}{|c|c|c|c|} \hline A& B& P(A,B)\\ \hline 0& 0 &.40\\ 0& 1 &.30\\ 1& 0 &.20\\ 1& 1 &.10\\ \hline \end{array} $$

It's clear that $P(A,B) \neq P(A)P(B)$ but if I wanted to draw a Bayesian belief network, how can I derive which variable is dependent on the other?

i.e. which of these two would be the correct belief network enter image description here

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  • $\begingroup$ Unless you have marginal distributions and/or make some assumptions such as discarding negative influence, I don't believe this is identifiable. $\endgroup$ – jkm Jan 10 at 14:42
  • $\begingroup$ @jkm Since the full joint distribution is known, the marginals are (easily) deducible. Exactly which marginal distributions are you referring to, then? $\endgroup$ – whuber Jan 10 at 14:43
  • $\begingroup$ Sorry, had a brain-fart. I meant the priors. $\endgroup$ – jkm Jan 10 at 15:03

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