Design of extended Neyman-Pearson hypothesis tests

Qian Zhang; Pramod K. Varshney; Yunmin Zhu

doi:10.1117/12.357178

27 July 1999 Design of extended Neyman-Pearson hypothesis tests

Qian Zhang, Pramod K. Varshney, Yunmin Zhu

Proceedings Volume 3720, Signal Processing, Sensor Fusion, and Target Recognition VIII; (1999) https://doi.org/10.1117/12.357178
Event: AeroSense '99, 1999, Orlando, FL, United States

Abstract

We consider a problem in which exactly one of the n+1 distinct signals {S₀, ...,S_n}, 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 P_f_i, i=1, ...,n, where P_f_i is the probability that S_i is declared as S₀, and the detection probability P_d which is the probability that S₀ is correctly recognized. It is required that P_d be maximized while P_f_i≤c_i, i=1,...,n, where c₁, ...,c_n are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p₀(x) is tested against (w₁p₁(x)+ ...+w_np_n(x)) where p_i(x) is the probability density function of observation X when S_i occurs. We propose two methods to obtain w₁, ..., w_n for any given c₁, ..., c_n. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w₁, ..., w_n which provides a sequence of extended Neyman-Pearson tests that converge to the optical solution. Numerical examples are given to illustrate these methods.

Citation Download Citation

Qian Zhang, Pramod K. Varshney, and Yunmin Zhu "Design of extended Neyman-Pearson hypothesis tests", Proc. SPIE 3720, Signal Processing, Sensor Fusion, and Target Recognition VIII, (27 July 1999); https://doi.org/10.1117/12.357178

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