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Compatible prior distributions for directed acyclic graph models

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The application of certain Bayesian techniques, such as the Bayes factor and model averaging, requires the specification of prior distributions on the parameters of alternative models. We propose a new method for constructing compatible priors on the parameters of models nested in a given directed acyclic graph model, using a conditioning approach. We define a class of parameterizations that is consistent with the modular structure of the directed acyclic graph and derive a procedure, that is invariant within this class, which we name reference conditioning.
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Keywords: Bayes factor; Directed acyclic graph; Fisher information matrix; Graphical model; Group reference prior; Invariance; Jeffreys conditioning; Reference conditioning; Reparameterization

Document Type: Research Article

Publication date: February 1, 2004

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