  Recovery of the causal structure of dynamic networks from noisy measurements
has long been a problem of intense interest across many areas of science and
engineering. Many algorithms have been proposed, but there is no work that
compares the performance of the algorithms to converse bounds in a
non-asymptotic setting. As a step to address this problem, this paper gives
lower bounds on the error probability for causal network support recovery in a
linear Gaussian setting. The bounds are based on the use of the Bhattacharyya
coefficient for binary hypothesis testing problems with mixture probability
distributions. Comparison of the bounds and the performance achieved by two
representative recovery algorithms are given for sparse random networks based
on the Erd\H{o}s-R\'enyi model.
