A distributed hypothesis-testing team decision problem with communications cost

In this paper we formulate and solve a distributed binary hypothesis-testing problem. We consider a cooperative team that consists of two decision makers (DM´s); one is refered to as the primary DM and the other as the consulting DM. The team objective is to carry out binary hypothesis testing based upon uncertain measurements. The primary DM can declare his decision based only on its own measurements; however, in ambiguous situations the primary DM can ask the consulting DM for an opinion and it incurs a communications cost. Then the consulting DM transmits either a definite recommendation or pleads ignorance. The primary DM has the responsibility of making a final definitive decision. The team objective is the minimization of the probability of error, taking into account different costs for hypothesis misclassification and communication costs. Numerical results are included to demonstrate the dependence of the different decision thresholds on the problem parameters, including different perceptions of the prior information.