Bayesian networks for fMRI: a primer.

Bayesian network analysis is an attractive approach for studying the functional integration of brain networks, as it includes both the locations of connections between regions of the brain (functional connectivity) and more importantly the direction of the causal relationship between the regions (directed functional connectivity). Further, these approaches are more attractive than other functional connectivity analyses in that they can often operate on larger sets of nodes and run searches over a wide range of candidate networks. An important study by Smith et al. (2011) illustrated that many Bayesian network approaches did not perform well in identifying the directionality of connections in simulated single-subject data. Since then, new Bayesian network approaches have been developed that have overcome the failures in the Smith work. Additionally, an important discovery was made that shows a preprocessing step used in the Smith data puts some of the Bayesian network methods at a disadvantage. This work provides a review of Bayesian network analyses, focusing on the methods used in the Smith work as well as methods developed since 2011 that have improved estimation performance. Importantly, only approaches that have been specifically designed for fMRI data perform well, as they have been tailored to meet the challenges of fMRI data. Although this work does not suggest a single best model, it describes the class of models that perform best and highlights the features of these models that allow them to perform well on fMRI data. Specifically, methods that rely on non-Gaussianity to direct causal relationships in the network perform well.