  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 non-neuronal
signals. By exploiting the experimental design, we propose to estimate
stimulus-locked brain network by treating non-stimulus-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 pre-specific 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.
