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I am interested in modeling a decision support system with a bayesian network, consisting of discrete random variables. While I could use CPT, the requirements grow exponentially in size so I am curious about a more tractable representation. I was suggested the multinomial Dirichlet distribution but decision support doesn't seem well represented as a multinomial Dirichlet distribution; that is viewing decision support as the number of successes for n number of trials seems odd. Are there any other discrete distributions commonly used in Bayesian networks proper for decision support? Am I incorrect to view multinomial Dirichlet as unsuited to decision support?

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The more tractable representation is the CPT as opposed to the full joint distribution which it succinctly represents. Often the Dirichlet distribution is used for this kind of problem.

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