2002-17: Compatible Prior Distributions for DAG models

DIMACS TR: 2002-17

Compatible Prior Distributions for DAG models

Authors: Alberto Roverato and Guido Consonni

ABSTRACT
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.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-17.ps.gz

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