  Circular variables such as phase or orientation have received considerable
attention throughout the scientific and engineering communities and have
recently been quite prominent in the field of neuroscience. While many analytic
techniques have used phase as an effective representation, there has been
little work on techniques that capture the joint statistics of multiple phase
variables. In this paper we introduce a distribution that captures empirically
observed pair-wise phase relationships. Importantly, we have developed a
computationally efficient and accurate technique for estimating the parameters
of this distribution from data. We show that the algorithm performs well in
high-dimensions (d=100), and in cases with limited data (as few as 100 samples
per dimension). We also demonstrate how this technique can be applied to
electrocorticography (ECoG) recordings to investigate the coupling of brain
areas during different behavioral states. This distribution and estimation
technique can be broadly applied to any setting that produces multiple circular
variables.
