Hierarchical Gaussian graphical models and group level networks
The Gaussian graphical model (GGM) is often used to estimate the network structure of high-dimensional data. However, the standard Gaussian graphical model does not describe hierarchical structures in the data, which frequently occur in empirical research. For example, in fMRI studies, each participant has an individual network, but participants are also related as they form a population. Nevertheless, a common approach to analyze such data is to fit a GGM for each participant individually, thereby neglecting the shared variance. This talk discusses an extension of the GGM that describes hierarchical data. We relate the networks of individuals using Markov random field priors on the edge structure. Specifically, we use the Ising model and the Curie-Weiss model as Markov random field priors. This approach simultaneously captures the shared variance between the graph structure of different individuals and estimates a group-level network. The method is illustrated with an application on resting state fMRI data.