Asypmtotically Optimal Decision among Several Hypotheses for Nonhomogeneous Gaussian Processes

We consider the problem of testing several simple hypotheses for a nonhomogeneous Gaussian process with different probabilities of an incorrect decision. An asymptotically optimal nonsequential decision rule is obtained assuming that the error probabilities tend to zero at an arbitrary rate. The characteristics of the decision rule are determined and it is compared with the maximum likelihood algorithm.