Abstract
This chapter talks about various approaches to parameterizing graphical models. It begins with the hyper-Dirichlet distribution, the natural conjugate distribution for the discrete Bayesian network. However, the hyper-Dirichlet has many parameters as table size increases, and it is often difficult to assess hyper-Dirichlet priors. The chapter thus explores two different approaches to reducing the number of parameters in the model. First are models that add a layer of probabilistic noise to logical functions such as AND and OR gates, producing the kinds of link functions seen in cognitive diagnosis. Second are models that use functions from normal regression theory and item response theory (such as Samejima's graded response model) to model probability tables more parsimoniously.
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