Differential privacy in parallel distributed Bayesian detections

In this paper, the differential privacy problem in parallel distributed detections is studied in the Bayesian formulation. The privacy risk is evaluated by the minimum detection cost for the fusion node to infer the private random phenomenon. Different from the privacy-unconstrained distributed Bayesian detection problem, the optimal operation point of a remote decision maker can be on the boundary of the privacy-unconstrained operation region or in the intersection of privacy constraint hyperplanes. Therefore, for a remote decision maker in the optimal privacy-constrained distributed detection design, it is sufficient to consider a deterministic linear likelihood combination test or a randomized decision strategy of two linear likelihood combination tests which achieves the optimal operation point in each case. Such an insight indicates that the existing algorithm can be reused by incorporating the privacy constraint. The trade-off between detection and privacy metrics will be illustrated in a numerical example.