A Decision-Theory Approach to Missile Defense

The defense being attacked by a warhead concealed in a cloud of decoys has a problem that belongs in the realm of decision theory. Here it is assumed that the defense gets one measurement on each object, this measurement is subject to error and it, thus considered a random variable. Measurements on decoys come from one distribution, those on warheads come from another. The total cloud is, thus a sample of which one element is the oddball, or outlier. This paper shows how to maximize the defensive probability of hitting the outlier under the two situations first, with the objects strung out so they must be treated sequentially, second, when all the objects appear at once.