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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Neyman, J., and Pearson, E. S., Phil. Trans. Roy. Soc., A, 231, 289 (1933).
For exposition and bibliography, see Peterson, W. W., Birdsall, T. G., and Fox, W. C., Trans. Inst. Radio Eng., PGIT-4, 171 (Sept. 1954), also Middleton, D., An Introduction to Statistical Communication Theory, Chap. 19 (McGraw-Hill, New York, 1960).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
RUDNICK, P. A Signal-to-Noise Property of Binary Decisions. Nature 193, 604–605 (1962). https://doi.org/10.1038/193604a0
Issue Date:
DOI: https://doi.org/10.1038/193604a0
This article is cited by
-
On the detectabillity limit of coherent optical signals in thermal radiation
Journal of Statistical Physics (1970)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.