  In many applications we have both observational and (randomized)
interventional data. We propose a Gaussian likelihood framework for joint
modeling of such different data-types, based on global parameters consisting of
a directed acyclic graph (DAG) and correponding edge weights and error
variances. Thanks to the global nature of the parameters, maximum likelihood
estimation is reasonable with only one or few data points per intervention. We
prove consistency of the BIC criterion for estimating the interventional Markov
equivalence class of DAGs which is smaller than the observational analogue due
to increased partial identifiability from interventional data. Such an
improvement in identifiability has immediate implications for tighter bounds
for inferring causal effects. Besides methodology and theoretical derivations,
we present empirical results from real and simulated data.
