Letter | Published:

A Signal-to-Noise Property of Binary Decisions

Nature volume 193, pages 604605 (10 February 1962) | Download Citation

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Abstract

THE statistical theory of Neyman and Pearson1, which uses the likelihood ratio in making binary decisions, has proved very valuable when applied to the physical problem of detecting a signal in noise2. This theory uses error probabilities as the basic criterion of performance in detection and tends to suggest that the attention given to the signal-to-noise ratio in older approaches is now outmoded. The purpose of this communication is to point out that, while a maximum signal-to-noise property is not any longer to be considered necessary in an optimum receiver for detection, a suitably formulated signal-to-noise requirement is sufficient to lead to a likelihood ratio receiver. This conclusion rests on a fully general property of the Neyman–Pearson binary decision theory which seems to have escaped previous notice.

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References

  1. 1.

    , and , Phil. Trans. Roy. Soc., A, 231, 289 (1933).

  2. 2.

    For exposition and bibliography, see , , and , Trans. Inst. Radio Eng., PGIT-4, 171 (Sept. 1954), also , An Introduction to Statistical Communication Theory, Chap. 19 (McGraw-Hill, New York, 1960).

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Affiliations

  1. University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego 52, California.

    • PHILIP RUDNICK

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https://doi.org/10.1038/193604a0

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