Review:NP theorem NP Theorem:Likelihood ratio test(LRT) maximize Pp while a given PrA=a,decide H if L(x)= P(x;H) P(x;Ho) The threshold y is determined from PrA as p(x;Ho)dx a L(x):the likelihood ratio n-xaxH放 whxiong@uestc.edu.cn 8whxiong@uestc.edu.cn Review: NP theorem NP Theorem: Likelihood ratio test (LRT) • maximize PD while a given PFA =α , decide H1 if 8 L(x) = P(x; H1) P(x; H0) > ° The threshold γ is determined from PFA as PFA = Z x:L(x)>° p(x; H0)dx = ® L(x): the likelihood ratio PD = Z x:L(x)>° p(x; H1)dx