Bayesian network detection using absorbing Markov chains

A Bayesian framework for network detection is developed based on random walks on graphs. Networks are detected using partial observations of their activity, and the Bayesian approach is proved to be optimum in the Neyman-Pearson sense, assuming random walk propagation on a given graph and diffusion model with absorbing states. The equivalence of the random walk and harmonic solutions to the Bayesian formulation is proven. A general diffusion model is introduced that utilizes spatio-temporal relationships between vertices, and is used for a specific space-time formulation that leads to significant performance improvements.