Randomization in distributed detection

The design of optimal decentralized detectors requires simultaneous optimization both of quantizer mappings for the individual sensors and of the global fusion rule. It is shown that if the likelihood ratios of the unquantized (or raw) observations contain no point-masses of probability, the optimal test does not randomize; this is so despite the fact that the data to be used can be considered discrete. Since of an uncountably infinite number of fusion rules only a finite few are admissible candidates, this results in a considerable simplification in design algorithms