Learning-Based Epsilon Most Stringent Test for Gaussian Samples Classification

This paper studies the problem of classifying some Gaussian samples into one of two parametric probabilistic models, also called sources, when the parameter and the a priori probability of each source are unknown. Each source is governed by an univariate normal distribution whose mean is unknown. A training sequence is available for each source in order to compensate the lack of prior information. An almost optimal most stringent test is proposed to solve this classification problem subject to a constrained false alarm probability. This learning-based test minimizes its maximum shortcoming with respect to the most powerful test which knows exactly the parameters of the sources. It also guarantees a prescribed false alarm probability whatever the size of the training sequences. The threshold, the probability of false alarm and the probability of correct detection are calculated analytically.