  Networks - collections of interacting elements or nodes - abound in the
natural and manmade worlds. For many networks, complex spatiotemporal dynamics
stem from patterns of physical interactions unknown to us. To infer these
interactions, it is common to include edges between those nodes whose time
series exhibit sufficient functional connectivity, typically defined as a
measure of coupling exceeding a pre-determined threshold. However, when
uncertainty exists in the original network measurements, uncertainty in the
inferred network is likely, and hence a statistical propagation-of-error is
needed. In this manuscript, we describe a principled and systematic procedure
for the inference of functional connectivity networks from multivariate time
series data. Our procedure yields as output both the inferred network and a
quantification of uncertainty of the most fundamental interest: uncertainty in
the number of edges. To illustrate this approach, we apply our procedure to
simulated data and electrocorticogram data recorded from a human subject during
an epileptic seizure. We demonstrate that the procedure is accurate and robust
in both the determination of edges and the reporting of uncertainty associated
with that determination.
