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Percolation on complex networks has been used to study computer viruses,epidemics, and other casual processes. Here, we present conditions for theexistence of a network specific, observation dependent, phase transition in theupdated posterior of node states resulting from actively monitoring thenetwork. Since traditional percolation thresholds are derived using observationindependent Markov chains, the threshold of the posterior should moreaccurately model the true phase transition of a network, as the updatedposterior more accurately tracks the process. These conditions should provideinsight into modeling the dynamic response of the updated posterior to activeintervention and control policies while monitoring large complex networks.

Percolation Thresholds of Updated Posteriors for Tracking Causal Markov Processes in Complex Networks