Estimating and inferring the maximum degree of stimulus‐locked time‐varying brain connectivity networks

Neuroscientists have enjoyed much success in understanding brain functions by constructing brain connectivity networks using data collected under highly controlled experimental settings. However, these experimental settings bear little resemblance to our real‐life experience in day‐to‐day interactions with the surroundings. To address this issue, neuroscientists have been measuring brain activity under natural viewing experiments in which the subjects are given continuous stimuli, such as watching a movie or listening to a story. The main challenge with this approach is that the measured signal consists of both the stimulus‐induced signal, as well as intrinsic‐neural and nonneuronal signals. By exploiting the experimental design, we propose to estimate stimulus‐locked brain networks by treating nonstimulus‐induced signals as nuisance parameters. In many neuroscience applications, it is often important to identify brain regions that are connected to many other brain regions during cognitive process. We propose an inferential method to test whether the maximum degree of the estimated network is larger than a prespecific number. We prove that the type I error can be controlled and that the power increases to one asymptotically. Simulation studies are conducted to assess the performance of our method. Finally, we analyze a functional magnetic resonance imaging dataset obtained under the Sherlock Holmes movie stimuli.