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?
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.