  Describing the causal relations governing a system is a fundamental task in
many scientific fields, ideally addressed by experimental studies. However,
obtaining data under intervention scenarios may not always be feasible, while
discovering causal relations from purely observational data is notoriously
challenging. In certain settings, such as genomics, we may have data from
heterogeneous study conditions, with soft (partial) interventions only
pertaining to a subset of the study variables, whose effects and targets are
possibly unknown. Combining data from experimental and observational studies
offers the opportunity to leverage both domains and improve on the
identifiability of causal structures. To this end, we define the interventional
BGe score for a mixture of observational and interventional data, where the
targets and effects of intervention may be unknown. To demonstrate the approach
we compare its performance to other state-of-the-art algorithms, both in
simulations and data analysis applications. Prerogative of our method is that
it takes a Bayesian perspective leading to a full characterisation of the
posterior distribution of the DAG structures. Given a sample of DAGs one can
also automatically derive full posterior distributions of the intervention
effects. Consequently the method effectively captures the uncertainty both in
the structure and the parameter estimates. Codes to reproduce the simulations
and analyses are publicly available at github.com/jackkuipers/iBGe
