  Functional brain networks can change rapidly as a function of stimuli or
cognitive shifts. Tracking dynamic functional connectivity is particularly
challenging as it requires estimating the structure of the network at each
moment as well as how it is shifting through time. In this paper, we describe a
general modeling framework and a set of specific models that provides
substantially increased statistical power for estimating rhythmic dynamic
networks, based on the assumption that for a particular experiment or task, the
network state at any moment is chosen from a discrete set of possible network
modes. Each model is comprised of three components: (1) a set of latent
switching states that represent transitions between the expression of each
network mode; (2) a set of latent oscillators, each characterized by an
estimated mean oscillation frequency and an instantaneous phase and amplitude
at each time point; and (3) an observation model that relates the observed
activity at each electrode to a linear combination of the latent oscillators.
We develop an expectation-maximization procedure to estimate the network
structure for each switching state and the probability of each state being
expressed at each moment. We conduct a set of simulation studies to illustrate
the application of these models and quantify their statistical power, even in
the face of model misspecification.
