Privacy-Aware Distributed Bayesian Detection

We study the eavesdropping problem in the remotely distributed sensing of a privacy-sensible hypothesis from the Bayesian detection perspective. We consider a parallel distributed detection network where remote decision makers independently make local decisions defined on finite domains and forward them to the fusion center which makes the final decision. An eavesdropper is assumed to intercept a specific set of local decisions to make also a guess on the hypothesis. We propose a novel Bayesian detection-operational privacy metric given by the minimal achievable Bayesian risk of the eavesdropper. Further, we introduce two privacy-aware distributed Bayesian detection formulations, namely the privacy-constrained distributed Bayesian detection problem and the privacy-concerned distributed Bayesian detection problem where the detection performance is optimized under a privacy guarantee constraint and a weighted sum objective of the detection performance and privacy risk is minimized respectively. For an optimal privacy-aware distributed Bayesian detection design, the optimal decision strategy of employing a deterministic likelihood test or a randomized strategy thereof is identified. Further, it is shown that equivalent problems of different formulations always exist and lead to the same optimal privacy-aware distributed Bayesian detection design. The results are illustrated and discussed by numerical examples. The idea of privacy-aware distributed Bayesian detection design provides a novel solution to realize future trustworthy Internet of Things applications.