Compatible Prior Distributions for DAG models

Compatible Prior Distributions for DAG models (2002)

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by Alberto Roverato , Guido Consonni

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BibTeX

@MISC{Roverato02compatibleprior,
    author = {Alberto Roverato and Guido Consonni},
    title = {Compatible Prior Distributions for DAG models},
    year = {2002}
}

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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.

Citations

848	Graphical Models - Lauritzen - 1996
787	Field Theory - Wit, Smith - 1986
766	Causality: Models, Reasoning, and Inference - Pearl
752	Learning Bayesian networks: The combination of knowledge and statistical data - Heckerman, Geiger, et al. - 1995
717	Bayes factors - Kass, Raftery - 1995
500	Probabilistic Networks and Expert Systems - Cowell, Dawid, et al. - 1999
384	Causation, prediction and search - Spirtes, Glymour, et al. - 1993
179	Equivalence and synthesis of causal models - Verma, Pearl
177	Sequential updating of conditional probabilities on directed graphical structures - Spiegelhalter, Lauritzen - 1990
143	Covariance selection - Dempster - 1972
102	Handbook of Matrices - Lutkepohl - 1996
89	Reference posterior distributions for Bayesian inference (with discussion - Bernardo - 1979
46	Causal inference from graphical models - Lauritzen - 2001
33	Some matrix-variate distribution theory: Notational considerations and a Bayesian application - Dawid - 1981
32	Chain graph models and their causal interpretations - Lauritzen, Richardson
24	Hyper inverse wishart distribution for non-decomposable graphs and its application to bayesian inference for gaussian graphical models - Roverato - 2002
23	On the Markov equivalence of chain graphs, undirected graphs, and acyclic digraphs - Andersson, Madigan, et al. - 1997
23	Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Annals of statistics 30(5 - Geiger, Heckerman - 2002
23	Linear recursive equations, covariance selection, and path analysis - Wermuth - 1980
18	On the development of reference prior method - Berger, Bernardo - 1992
17	On the invariance of noninformative priors - Datta, Ghosh - 1995
13	Some remarks on noninformative priors - Datta, Ghosh - 1995
11	Cholesky decomposition of a hyper inverse Wishart matrix - Roverato - 2000
8	Analogies between multiplicative models in contingency tables and covariance selection. Biometrics 32: 95 - Wermuth - 1976
7	Compatible prior distributions - Dawid, Lauritzen - 2001
5	The Isserlis matrix and its application to non-decomposable graphical Gaussian models - Roverato, Whittaker - 1998
3	Enriched conjugate and reference priors for the Wishart family on symmetric cones - Consonni, Veronese - 2003
2	Reference priors for exponential families - Gutierrez-Pena, Rueda - 2002
2	Conjugate parameterizations for natural exponential families - Gutierrez-Pena, Smith - 1995