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Network theoretic analysis of maximum a posteriori detectors for optimal input detection

Abstract:

We study maximum-a-posteriori detectors to detect changes in the constant mean vector and the covariance matrix of a Gaussian stationary stochastic input driving a few nodes in a network, using remotely located sensor measurements. We show that the detectors’ performance can be analyzed using specific input-to-output gain of the network system's transfer function matrix and the input statistics and sensor noise in the asymptotic measurement regime. Using this result, we study the detector's performance using node cutsets that separate the nodes containing inputs from a partitioned set of nodes not containing inputs. In the absence of noise, we show that the detectors’ performance is no better for sensors on a partitioned set than those on the cutset. Instead, in the presence of noise, we show that the detectors’ performance can be better for sensors on a partitioned set than those on the cutset for certain choices of edge weights. Our results quantify the extent to which input and sensor nodes’ distance modulates detection performance via separating cutsets, and have potential applications in sensor placement problems. Finally, we complement the theory with simulations.