Caprice 1-2

### Torus Graphs for Multivariate Phase Coupling Analysis (304885)

**Natalie E Klein, Carnegie Mellon University*

*Josue Orellana, Carnegie Mellon University*

*Scott Brincat, The Picower Institute for Learning and Memory, Massachusetts Institute of Technology*

*Earl K Miller, The Picower Institute for Learning and Memory, Massachusetts Institute of Technology*

*Robert E Kass, Carnegie Mellon University*

**Keywords:** Graphical models, circular statistics, neuroscience

Distinct brain areas communicate during performance of a task, during which signals recorded from particular brain areas have been observed to have substantial power within specific bands, indicating oscillatory behavior. There is great interest in identifying consistent phase relationships of oscillations in distinct areas, which suggest cross-area cooperation. A thorough description of such cross-area interactions would then be based on a graph, where each node represents the phase of an oscillation in a particular brain area, and each edge corresponds to some measure of association. However, Gaussian graphical models can not solve this problem because angles are topologically circular. We have developed the appropriate analogue of Gaussian graphical models, which we call Torus Graphs. Each torus graphical model is an exponential family on a multidimensional torus. We show how statistical inferences in this setting can be produced, and lead to interesting descriptions of brain region interactions in the context of an experiment on associative memory. This framework also unifies, and improves understanding of many methods that have appeared previously in circular statistics.