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I have some trouble understanding the benefits of Bayesian networks.

Am I correct that the key benefit of the network is that one does not need to use chain rule of probability in order to calculate joint distributions?

So, using the chain rule:

$$ P(A_1, \dots, A_n) = \prod_{i=1}^n (A_i \mid \cap_{j=1}^{i-1} A_j) $$

leads to the same result as the following (assuming the nodes are structured by an Bayesian network)?

$$ P(A_1, \dots, A_n) = \prod_{i=1}^n P(A_i \mid \text{parents}(A_i)) $$

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  • $\begingroup$ One other thing that comes to mind is markov blankets and other conditional independences, so local information is sufficient and other nodes are conditionally independent. I am not experienced enough to say how this is applied, but you can search for that. Having a Bayesian network feels to me like when I'm happy when I can use a Markov chain as a model, because of the structure and simplified dependencies. Judea Pearl, the man who introduced these networks, can explain this much better I'm sure: edge.org/conversation/judea_pearl-engines-of-evidence $\endgroup$ – PHPirate Feb 20 at 9:44
  • $\begingroup$ @Sebastian benefit compared to what? $\endgroup$ – mshlis Jul 28 at 18:04

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