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Time Varying Functional Connectivity (TVFC) investigates how the interactionsamong brain regions vary over the course of an fMRI experiment. The transitionsbetween different individual connectivity states can be modulated by changes inunderlying physiological mechanisms that drive functional network dynamics,e.g., changes in attention or cognitive effort as measured by pupil dilation.In this paper, we develop a multi-subject Bayesian framework for estimatingdynamic functional networks as a function of time-varying exogenousphysiological covariates that are simultaneously recorded in each subjectduring the fMRI experiment. More specifically, we consider a dynamic Gaussiangraphical model approach, where a non-homogeneous hidden Markov model isemployed to classify the fMRI time series into latent neurological states,borrowing strength over the entire time course of the experiment. Thestate-transition probabilities are assumed to vary over time and acrosssubjects, as a function of the underlying covariates, allowing for theestimation of recurrent connectivity patterns and the sharing of networks amongthe subjects. Our modeling approach further assumes sparsity in the networkstructures, via shrinkage priors. We achieve edge selection in the estimatedgraph structures, by introducing a multi-comparison procedure forshrinkage-based inferences with Bayesian false discovery rate control. We applyour modeling framework on a resting-state experiment where fMRI data have beencollected concurrently with pupillometry measurements, leading us to assess theheterogeneity of the effects of changes in pupil dilation, previously linked tochanges in norepinephrine-containing locus coeruleus, on the subjects'propensity to change connectivity states.

A Predictor-Informed Multi-Subject Bayesian Approach for Dynamic Functional Connectivity