  The problem of detecting changes with multiple sensors has received
significant attention in the literature. In many practical applications such as
critical infrastructure monitoring and modeling of disease spread, a useful
change propagation model is one where change eventually happens at all sensors,
but where not all sensors witness change at the same time instant. While prior
work considered the case of known change propagation dynamics, this paper
studies a more general setting of unknown change propagation pattern
(trajectory). A Bayesian formulation of the problem in both centralized and
decentralized settings is studied with the goal of detecting the first time
instant at which any sensor witnesses a change. Using the dynamic programming
(DP) framework, the optimal solution structure is derived and in the rare
change regime, several more practical change detection algorithms are proposed.
Under certain conditions, the first-order asymptotic optimality of a proposed
algorithm called multichart test is shown as the false alarm probability
vanishes. To further reduce the computational complexity, change detection
algorithms are proposed based on online estimation of the unknown change
propagation pattern. Numerical studies illustrate that the proposed detection
techniques offer near-optimal performance. Further, in the decentralized
setting, it is shown that if an event-triggered sampling scheme called
level-crossing sampling with hysteresis (LCSH) is used for sampling and
transmission of local statistics, the detection performance can be
significantly improved using the same amount of communication resources
compared to the conventional uniform-in-time sampling (US) scheme.
