# Detecting the dependency of a probability distribution

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

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