Some properties of optimal thresholds in decentralized detection

A decentralized Bayesian hypothesis testing problem is considered. It is analytically demonstrated that for the binary hypothesis problem, when there are two sensors with statistically independent Gaussian-distributed 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 a optimal set of decision rules.