On the design of extended Neyman-Pearson hypothesis tests

Qian Zhang, Pramod Kumar Varshney, Yunmin Zhu

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider a problem in which exactly one of n+1 distinct signals {S0, ..., Sn}, say S0, may be present in a noisy environment and the presence or absence of S0 needs to be determined. The performance is given by the false alarm probabilities Pf(i), i = 1, ..., n, where Pf(i) is the probability that Si is declared as S0, and the detection probability Pd which is the probability that S0 is correctly recognized. It is required that Pd be maximized while Pf(i)≤ci, i = 1, ..., n, where c1, ..., cn are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p0(x) is tested against (w1p1(x)+...+wnpn(x)) where pi(x) is the probability density function of observation X when Si occurs. We propose two methods to obtain w1, ..., wn for any given c1, ..., cn. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w1, ..., wn which provides a sequence of extended Neyman-Pearson tests that converge to the optimal solution. Numerical examples are given to illustrate these methods.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherSociety of Photo-Optical Instrumentation Engineers
Pages378-389
Number of pages12
Volume3720
StatePublished - 1999
EventProceedings of the 1999 Signal Processing, Sensor Fusion, and Target Recognition VIII - Orlando, FL, USA
Duration: Apr 5 1999Apr 7 1999

Other

OtherProceedings of the 1999 Signal Processing, Sensor Fusion, and Target Recognition VIII
CityOrlando, FL, USA
Period4/5/994/7/99

Fingerprint

false alarms
probability density functions
Probability density function

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Zhang, Q., Varshney, P. K., & Zhu, Y. (1999). On the design of extended Neyman-Pearson hypothesis tests. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 3720, pp. 378-389). Society of Photo-Optical Instrumentation Engineers.

On the design of extended Neyman-Pearson hypothesis tests. / Zhang, Qian; Varshney, Pramod Kumar; Zhu, Yunmin.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3720 Society of Photo-Optical Instrumentation Engineers, 1999. p. 378-389.

Research output: Chapter in Book/Report/Conference proceedingChapter

Zhang, Q, Varshney, PK & Zhu, Y 1999, On the design of extended Neyman-Pearson hypothesis tests. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 3720, Society of Photo-Optical Instrumentation Engineers, pp. 378-389, Proceedings of the 1999 Signal Processing, Sensor Fusion, and Target Recognition VIII, Orlando, FL, USA, 4/5/99.
Zhang Q, Varshney PK, Zhu Y. On the design of extended Neyman-Pearson hypothesis tests. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3720. Society of Photo-Optical Instrumentation Engineers. 1999. p. 378-389
Zhang, Qian ; Varshney, Pramod Kumar ; Zhu, Yunmin. / On the design of extended Neyman-Pearson hypothesis tests. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3720 Society of Photo-Optical Instrumentation Engineers, 1999. pp. 378-389
@inbook{c7d907dd91114c748ef9f8a39d413b8b,
title = "On the design of extended Neyman-Pearson hypothesis tests",
abstract = "We consider a problem in which exactly one of n+1 distinct signals {S0, ..., Sn}, say S0, may be present in a noisy environment and the presence or absence of S0 needs to be determined. The performance is given by the false alarm probabilities Pf(i), i = 1, ..., n, where Pf(i) is the probability that Si is declared as S0, and the detection probability Pd which is the probability that S0 is correctly recognized. It is required that Pd be maximized while Pf(i)≤ci, i = 1, ..., n, where c1, ..., cn are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p0(x) is tested against (w1p1(x)+...+wnpn(x)) where pi(x) is the probability density function of observation X when Si occurs. We propose two methods to obtain w1, ..., wn for any given c1, ..., cn. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w1, ..., wn which provides a sequence of extended Neyman-Pearson tests that converge to the optimal solution. Numerical examples are given to illustrate these methods.",
author = "Qian Zhang and Varshney, {Pramod Kumar} and Yunmin Zhu",
year = "1999",
language = "English (US)",
volume = "3720",
pages = "378--389",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "Society of Photo-Optical Instrumentation Engineers",

}

TY - CHAP

T1 - On the design of extended Neyman-Pearson hypothesis tests

AU - Zhang, Qian

AU - Varshney, Pramod Kumar

AU - Zhu, Yunmin

PY - 1999

Y1 - 1999

N2 - We consider a problem in which exactly one of n+1 distinct signals {S0, ..., Sn}, say S0, may be present in a noisy environment and the presence or absence of S0 needs to be determined. The performance is given by the false alarm probabilities Pf(i), i = 1, ..., n, where Pf(i) is the probability that Si is declared as S0, and the detection probability Pd which is the probability that S0 is correctly recognized. It is required that Pd be maximized while Pf(i)≤ci, i = 1, ..., n, where c1, ..., cn are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p0(x) is tested against (w1p1(x)+...+wnpn(x)) where pi(x) is the probability density function of observation X when Si occurs. We propose two methods to obtain w1, ..., wn for any given c1, ..., cn. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w1, ..., wn which provides a sequence of extended Neyman-Pearson tests that converge to the optimal solution. Numerical examples are given to illustrate these methods.

AB - We consider a problem in which exactly one of n+1 distinct signals {S0, ..., Sn}, say S0, may be present in a noisy environment and the presence or absence of S0 needs to be determined. The performance is given by the false alarm probabilities Pf(i), i = 1, ..., n, where Pf(i) is the probability that Si is declared as S0, and the detection probability Pd which is the probability that S0 is correctly recognized. It is required that Pd be maximized while Pf(i)≤ci, i = 1, ..., n, where c1, ..., cn are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p0(x) is tested against (w1p1(x)+...+wnpn(x)) where pi(x) is the probability density function of observation X when Si occurs. We propose two methods to obtain w1, ..., wn for any given c1, ..., cn. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w1, ..., wn which provides a sequence of extended Neyman-Pearson tests that converge to the optimal solution. Numerical examples are given to illustrate these methods.

UR - http://www.scopus.com/inward/record.url?scp=0032685641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032685641&partnerID=8YFLogxK

M3 - Chapter

VL - 3720

SP - 378

EP - 389

BT - Proceedings of SPIE - The International Society for Optical Engineering

PB - Society of Photo-Optical Instrumentation Engineers

ER -