Studying effective brain connectivity using multiregression dynamic models

A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents multiple dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian Networks, the hypothesised relationships accommodate conditional conjugate inference. We demonstrate for the first time how it is straightforward to search over all possible connectivity networks with dynamically changing intensity of transmission to find the Maximum a Posteriori Probability (MAP) model within this class. This search method is made feasible by using a novel application of the integer programming algorithm. The search over all possible directed (acyclic or cyclic) graphical structures can be made especially fast by utilising the fact that, within this class of models, the joint likelihood factorizes. We proceed to show how diagnostic methods, analogous to those defined for static Bayesian Networks, can be used to suggest embellishment of the model class to extend the process of model selection. A typical goal of experimental neuroscience is to draw conclusions regarding the causal mechanisms that underpin neural communication. Often the main focus of interest in these experiments includes not only a search for the likely model of a specific individual, but an analysis of shared between-subject e↵ects. Currently, such features are analysed using rather coarse aggregation methods over shared time series. However, here we demonstrate that, using the estimation of multiple causal graphical models and Bayesian hyperclustering techniques, it is possible to use the full machinery of Bayesian methods to formally make inferences in a coherent way which contemplates hypotheses about shared dependences between such populations of subjects. Methods developed here are illustrated using simulated and real resting-state and steady-state task functional Magnetic Resonance Imaging (fMRI) data