  This paper considers maximum-a-posteriori (MAP) and linear discriminant based
MAP detectors to detect changes in the mean and covariance of a stochastic
input, driving specific network nodes, using noisy measurements from sensors
non-collocated with the input nodes. We explicitly characterize both detectors'
performance in terms of the network edge weights and input and sensor nodes'
location. In the asymptotic measurement regime, when the input and measurement
noise are jointly Gaussian, we show that the detectors' performance can be
studied using the input to output gain of the system's transfer function
matrix. Using this result, we obtain conditions for which the detection
performance associated with the sensors on a given network cut is better (or
worse) than that of the sensors associated with the subnetwork induced by the
cut and not containing the input nodes. Our results also provide structural
insights into the sensor placement from a detection-theoretic viewpoint. We
validate our theoretical findings via multiple numerical examples.
