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A Bayesian belief network is a model of a joint distribution over a finiteset of variables, with a DAG structure representing immediate dependenciesamong the variables. For each node, a table of parameters (CPtable) representslocal conditional probabilities, with rows indexed by conditioning events(assignments to parents). CP-table rows are usually modeled as independentrandom vectors, each assigned a Dirichlet prior distribution. The assumptionthat rows are independent permits a relatively simple analysis but may notreflect actual prior opinion about the parameters. Rows representing similarconditioning events often have similar conditional probabilities. This paperintroduces a more flexible family of "dependent Dirichlet" prior distributions,where rows are not necessarily independent. Simple methods are developed toapproximate the Bayes estimators of CP-table parameters with optimal linearestimators; i.e., linear combinations of sample proportions and prior means.This approach yields more efficient estimators by sharing information amongrows. Improvements in efficiency can be substantial when a CP-table has manyrows and samples sizes are small.

Dependent Dirichlet Priors and Optimal Linear Estimators for Belief Net Parameters