Hypotheses Testing in a Distributed Environment

The problem of optimum detection with n decentralized sensors selecting among m possible signals is considered from the decision theory point of view. The loss function is defined in terms of the decisions made by each observer and the transmitted signal. Then the average of this loss function is minimized. This leads to sets of coupled inequalities in terms of the likelihood ratio of each observer and the decisions made at the other sensors. This determines the structure of the optimum decentralized detection for an arbitrary number of sensors and an arbitrary number of possible signals. These results are valuable in numerous situations that may arise in large-scale and distributed systems.