On the design of extended Neyman-Pearson hypothesis tests

Qian Zhang, Pramod K. Varshney, Yunmin Zhu

Research output: Contribution to journalConference Articlepeer-review


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)
Pages (from-to)378-389
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 1999
EventProceedings of the 1999 Signal Processing, Sensor Fusion, and Target Recognition VIII - Orlando, FL, USA
Duration: Apr 5 1999Apr 7 1999

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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