Estimating and Inferring the Maximum Degree of Stimulus-Locked Time-Varying Brain Connectivity Networks

Neuroscientists have enjoyed much success in understanding brain functions by\nconstructing brain connectivity networks using data collected under highly\ncontrolled experimental settings. However, these experimental settings bear\nlittle resemblance to our real-life experience in day-to-day interactions with\nthe surroundings. To address this issue, neuroscientists have been measuring\nbrain activity under natural viewing experiments in which the subjects are\ngiven continuous stimuli, such as watching a movie or listening to a story. The\nmain challenge with this approach is that the measured signal consists of both\nthe stimulus-induced signal, as well as intrinsic-neural and non-neuronal\nsignals. By exploiting the experimental design, we propose to estimate\nstimulus-locked brain network by treating non-stimulus-induced signals as\nnuisance parameters. In many neuroscience applications, it is often important\nto identify brain regions that are connected to many other brain regions during\ncognitive process. We propose an inferential method to test whether the maximum\ndegree of the estimated network is larger than a pre-specific number. We prove\nthat the type I error can be controlled and that the power increases to one\nasymptotically. Simulation studies are conducted to assess the performance of\nour method. Finally, we analyze a functional magnetic resonance imaging dataset\nobtained under the Sherlock Holmes movie stimuli.\n