Some properties of optimal thresholds in decentralized detection

A decentralized Bayesian hypothesis testing problem is considered. It is analytically demonstrated that for the known signal in the Gaussian noise binary hypothesis problem, when there are two sensors with statistically independent identically distributed Gaussian observations (conditioned on the true hypothesis), there is no loss in optimality in using the same decision rule at both sensors. Also, a multiple hypothesis problem is considered; some structure is analytically established for an optimal set of decision rules.<
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