TY - JOUR
T1 - Objective Bayes factors for Gaussian directed acyclic graphical models
AU - Consonni, Guido
AU - La Rocca, L.
PY - 2012
Y1 - 2012
N2 - We propose an objective Bayesian method for the comparison of all Gaussian directed
acyclic graphical models defined on a given set of variables. The method, which is based on the notion
of fractional Bayes factor (BF), requires a single default (typically improper) prior on the space of
unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can
be set to its minimal value. We show that our approach produces genuine BFs. The implied prior
on the concentration matrix of any complete graph is a data-dependent Wishart distribution, and
this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood.
We specialize our results to the smaller class of Gaussian decomposable undirected graphical
models and show that in this case they coincide with those recently obtained using limiting versions
of hyper-inverse Wishart distributions as priors on the graph-constrained covariance matrices
AB - We propose an objective Bayesian method for the comparison of all Gaussian directed
acyclic graphical models defined on a given set of variables. The method, which is based on the notion
of fractional Bayes factor (BF), requires a single default (typically improper) prior on the space of
unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can
be set to its minimal value. We show that our approach produces genuine BFs. The implied prior
on the concentration matrix of any complete graph is a data-dependent Wishart distribution, and
this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood.
We specialize our results to the smaller class of Gaussian decomposable undirected graphical
models and show that in this case they coincide with those recently obtained using limiting versions
of hyper-inverse Wishart distributions as priors on the graph-constrained covariance matrices
KW - Bayesian model selection
KW - Structural learning
KW - fractional Bayes factor
KW - Bayesian model selection
KW - Structural learning
KW - fractional Bayes factor
UR - http://hdl.handle.net/10807/43121
UR - http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9469.2011.00785.x/abstract
U2 - 10.1111/j.1467-9469.2011.00785.x
DO - 10.1111/j.1467-9469.2011.00785.x
M3 - Article
SN - 0303-6898
VL - 39
SP - 743
EP - 756
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
ER -