Privacy-concerned parallel distributed Bayesian sequential detection

In this paper, eavesdropping in parallel distributed sequential detections is considered. The privacy risk is evaluated by the minimal achievable Bayesian risk of a greedy and informed eavesdropper who is curious about the hypothesis realization. We propose a novel metric based on Bayesian risk to take the detection performance and privacy risk with different weights into account. We formulate and study the privacy-concerned parallel distributed Bayesian sequential detection problem under a finite time-horizon assumption. Solving this problem will lead to the optimal distributed sequential detection design which achieves the minimal privacy-concerned Bayesian risk. The study shows that it is not sufficient to consider a deterministic likelihood-ratio test for a remote decision maker at an active time index in the optimal privacy-concerned system design. However, properties of the optimal design indicate that the standard method can be extended to solve the proposed problem.