Least favorable distributions for the design of sensor detection systems in non-circular regions of interest

When designing a sensor system to detect the presence of an emitter whose random location has an unknown distribution, least favorable distributions can be used to avoid complications associated with composite hypotheses. Furthermore, sufficient conditions exist under which the least favorable distribution for the emitter location also makes the measurements conditionally independent and identically distributed, avoiding complications associated with conditionally dependent measurements. One such sufficient condition is having the region of interest be circular. We show that it is not trivial to extend this result to non-circular regions, and we identify a new set of sufficient conditions for a large set of non-circular regions. We also provide results to help choose among regions of interest.