  A new methodology for model determination in decomposable graphical Gaussian
models is developed. The Bayesian paradigm is used and, for each given graph, a
hyper inverse Wishart prior distribution on the covariance matrix is
considered. This prior distribution depends on hyper-parameters. It is
well-known that the models's posterior distribution is sensitive to the
specification of these hyper-parameters and no completely satisfactory method
is registered. In order to avoid this problem, we suggest adopting an empirical
Bayes strategy, that is a strategy for which the values of the hyper-parameters
are determined using the data. Typically, the hyper-parameters are fixed to
their maximum likelihood estimations. In order to calculate these maximum
likelihood estimations, we suggest a Markov chain Monte Carlo version of the
Stochastic Approximation EM algorithm. Moreover, we introduce a new sampling
scheme in the space of graphs that improves the add and delete proposal of
Armstrong et al. (2009). We illustrate the efficiency of this new scheme on
simulated and real datasets.
