  Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to
answer causal questions across a variety of scientific and social disciplines.
However, observational data alone cannot distinguish in general between DAGs
representing the same conditional independence assertions (Markov equivalent
DAGs); as a consequence the orientation of some edges in the graph remains
indeterminate. Interventional data, produced by exogenous manipulations of
variables in the network, enhance the process of structure learning because
they allow to distinguish among equivalent DAGs, thus sharpening causal
inference. Starting from an equivalence class of DAGs, a few procedures have
been devised to produce a collection of variables to be manipulated in order to
identify a causal DAG. Yet, these algorithmic approaches do not determine the
sample size of the interventional data required to obtain a desired level of
statistical accuracy. We tackle this problem from a Bayesian experimental
design perspective, taking as input a sequence of target variables to be
manipulated to identify edge orientation. We then propose a method to
determine, at each intervention, the optimal sample size capable of producing a
successful experiment based on a pre-experimental evaluation of the overall
probability of substantial correct evidence.
