  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 little work that
compares the performance of the algorithms to converse bounds. 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.
