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 DAG (Directed Acyclic Graph) model, using a conditioning
approach. We define a class of parameterisations consistent with the
modular structure of the DAG and derive a procedure, invariant within this
class, which we name reference conditioning.
Keywords: Bayes factor; Directed acyclic graph; Fisher information
matrix; Graphical model; Invariance; Jeffreys conditioning; Group
reference prior; Reference conditioning; Reparameterisation.
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