Neumann-Pearson criterion in pattern recognition

Let be Let us set a valid probability value after which we will look for such a boundary between images, which achieves the minimum .

Let it be required . Need to solve the problem of finding .

Clearly the solution satisfies the condition Indeed, with increases, that is, it becomes not the minimum possible, but with the restriction is violated . As in the minimax method, find analytically succeeds only in the simplest cases.