Constructing optimal classifiers from sub-optimal composite hypothesis tests

The general form of admissible solutions to classification problems depends on parameters πi whose values determine performance. However, translating performance requirements into parameter choices requires a difficult evaluation of interdependent probabilities. In this report we build optimal classifiers by combining composite hypothesis tests. The process relates the parameters πi to detection thresholds λ jk , which are more directly predictive of detection and false alarm probabilities. It is found that the constituent composite hypothesis tests cannot be optimal, but instead must be constructed via clairvoyant fusion principles.

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