Let's Not Waste Time: Using Temporal Information in Clustered Activity Estimation with Spatial Adjacency Restrictions (CAESAR) for Parcellating FMRI Data.

We have proposed a Bayesian approach for functional parcellation of whole-brain FMRI measurements which we call Clustered Activity Estimation with Spatial Adjacency Restrictions (CAESAR). We use distance-dependent Chinese restaurant processes (dd-CRPs) to define a flexible prior which partitions the voxel measurements into clusters whose number and shapes are unknown a priori. With dd-CRPs we can conveniently implement spatial constraints to ensure that our parcellations remain spatially contiguous and thereby physiologically meaningful. In the present work, we extend CAESAR by using Gaussian process (GP) priors to model the temporally smooth haemodynamic signals that give rise to the measured FMRI data. A challenge for GP inference in our setting is the cubic scaling with respect to the number of time points, which can become computationally prohibitive with FMRI measurements, potentially consisting of long time series. As a solution we describe an efficient implementation that is practically as fast as the corresponding time-independent non-GP model with typically-sized FMRI data sets. We also employ a population Monte-Carlo algorithm that can significantly speed up convergence compared to traditional single-chain methods. First we illustrate the benefits of CAESAR and the GP priors with simulated experiments. Next, we demonstrate our approach by parcellating resting state FMRI data measured from twenty participants as taken from the Human Connectome Project data repository. Results show that CAESAR affords highly robust and scalable whole-brain clustering of FMRI timecourses.