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Networks - collections of interacting elements or nodes - abound in thenatural and manmade worlds. For many networks, complex spatiotemporal dynamicsstem from patterns of physical interactions unknown to us. To infer theseinteractions, it is common to include edges between those nodes whose timeseries exhibit sufficient functional connectivity, typically defined as ameasure of coupling exceeding a pre-determined threshold. However, whenuncertainty exists in the original network measurements, uncertainty in theinferred network is likely, and hence a statistical propagation-of-error isneeded. In this manuscript, we describe a principled and systematic procedurefor the inference of functional connectivity networks from multivariate timeseries data. Our procedure yields as output both the inferred network and aquantification of uncertainty of the most fundamental interest: uncertainty inthe number of edges. To illustrate this approach, we apply our procedure tosimulated data and electrocorticogram data recorded from a human subject duringan epileptic seizure. We demonstrate that the procedure is accurate and robustin both the determination of edges and the reporting of uncertainty associatedwith that determination.

Network inference - with confidence - from multivariate time series