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Bugmaster comments on AI Risk & Opportunity: Strategic Analysis Via Probability Tree - Less Wrong
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Moving to a graph makes elicitation of the parameters a lot more difficult (to the extent that you have to start specifying clique potentials instead of conditional probabilities). Global tasks like marginalization or conditioning also become a lot harder.
I think you can still get away with using conditional probabilities if you make the graph directed and acyclical, as I should've specified (my bad). The graph is still more complex than the tree, as you said, but if we're using software for the tree, we might as well use one for the graph...