  Methodological development for the inference of gene regulatory networks from
transcriptomic data is an active and important research area. Several
approaches have been proposed to infer relationships among genes from
observational steady-state expression data alone, mainly based on the use of
graphical Gaussian models. However, these methods rely on the estimation of
partial correlations and are only able to provide undirected graphs that cannot
highlight causal relationships among genes. A major upcoming challenge is to
jointly analyze observational transcriptomic data and intervention data
obtained by performing knock-out or knock-down experiments in order to uncover
causal gene regulatory relationships. To this end, in this technical note we
present an explicit formula for the likelihood function for any complex
intervention design in the context of Gaussian Bayesian networks, as well as
its analytical maximization. This allows a direct calculation of the causal
effects for known graph structure. We also show how to obtain the Fisher
information in this context, which will be extremely useful for the choice of
optimal intervention designs in the future.
