  Reconstruction of a high-dimensional network may benefit substantially from
the inclusion of prior knowledge on the network topology. In the case of gene
interaction networks such knowledge may come for instance from pathway
repositories like KEGG, or be inferred from data of a pilot study. The Bayesian
framework provides a natural means of including such prior knowledge. Based on
a Bayesian Simultaneous Equation Model, we develop an appealing empirical Bayes
procedure which automatically assesses the relevance of the used prior
knowledge. We use variational Bayes method for posterior densities
approximation and compare its accuracy with that of Gibbs sampling strategy.
Our method is computationally fast, and can outperform known competitors. In a
simulation study we show that accurate prior data can greatly improve the
reconstruction of the network, but need not harm the reconstruction if wrong.
We demonstrate the benefits of the method in an analysis of gene expression
data from GEO. In particular, the edges of the recovered network have superior
reproducibility (compared to that of competitors) over resampled versions of
the data.
