The Empirical Bayes Solution of the Problem of Threshold Discrimination of Two Signals

V. L. Stefanyuk


Abstract: An algorithm for distinguishing two one-dimensional signals against a background of noise with unknown a priori signal probabilities is described. Consideration of the extremal properties of the distribution of the realizations at the receiver input and the use of an automaton with favorable behavior lead to the construction of a receiver which establishes the discrimination threshold automatically. A single number, the threshold value, is stored in the memory of the device. In its general features the algorithm is close to the methods of stochastic approximation [H. Robbins and S. Monro, Ann. Math. Stat., 1951, vol. 22, no. 1, pp. 400–407], but in distinction from the latter it does not contain a factor of "$1/n$ type" in the successive iterations, which permits us to hope that the algorithm will have some advantages in the solution of the empirical Bayes problem in situations where the a priori frequencies change with time. As an example, a generalization of the algorithm to physically real (multi-dimensional) problems is given. For simplicity the investigation is carried out using ideal observer criteria.

UDC: 621.391.14

Received: 16.04.1966

 English version: Problems of Information Transmission, 1967, 3:3, 5–13

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