A New Proof of the Neyman–Pearson Theorem Using the EEF and the Vindication of Sir R. Fisher

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The Neyman-Pearson theorem for the problem of simple hypothesis testing provides the fundamental approach to signal detection. In this letter we present a new proof that leverages the properties of exponential probability density function families and furthermore links parameter estimation to detection, a point of contention between Neyman-Pearson and Fisher. The new proof also provides corollaries concerning known properties of the receiver operating characteristics. Finally, a geometric interpretation to the problem of signal detection is given, which can provide much insight into its solution.