Compatible prior distributions for directed acyclic graph models

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2004 · Volume 66 · Issue 1

DOI: 10.1111/j.1467-9868.2004.00431.x

Abstract

Summary.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.

Keywords

Bayes factor, Directed acyclic graph, Fisher information matrix, Graphical model, Group reference prior, Invariance, Jeffreys conditioning, Reference conditioning, Reparameterization

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