A Bayesian Time-Varying Psychophysiological Interaction Model

Functional connectivity, the study of coordination between distinct brain regions, is a key focus in neuroscience. The Psychophysiological Interaction (PPI) model, commonly used to infer task-dependent functional connectivity, is limited by its susceptibility to confounding effects. We propose using partial correlations, instead of PPI regression coefficients, as they correct for confounding. We show how the PPI model can be used to estimate the precision matrix of a Gaussian Graphical Model (GGM), from which partial correlations are easily derived. We then propose a Bayesian extension to the PPI model that allows this measure of functional connectivity to vary over time. We enforce sparsity in the GGM precision matrix through scale-mixture shrinkage priors, mitigating overfitting. Additionally, we identify structural zeros in the precision matrix using a Bayesian multicomparison decision-theoretic framework. We demonstrate the efficacy of our model over the standard PPI model using simulated data and we further apply it to human fMRI data from a serial reaction time experiment. Our framework offers a more robust and dynamic approach to functional connectivity analysis.