  Inferring the causal structure of a system typically requires interventional
data, rather than just observational data. Since interventional experiments can
be costly, it is preferable to select interventions that yield the maximum
amount of information about a system. We propose a novel Bayesian method for
optimal experimental design by sequentially selecting interventions that
minimize the expected posterior entropy as rapidly as possible. A key feature
is that the method can be implemented by computing simple summaries of the
current posterior, avoiding the computationally burdensome task of repeatedly
performing posterior inference on hypothetical future datasets drawn from the
posterior predictive. After deriving the method in a general setting, we apply
it to the problem of inferring causal networks. We present a series of
simulation studies in which we find that the proposed method performs favorably
compared to existing alternative methods. Finally, we apply the method to real
and simulated data from a protein-signaling network.

Methodology