NP theorem (3/7) NP Theorem:Likelihood ratio test(LRT) maximize Pp for a given PEA=a,decide H if whxiong@uestc.edu.cn 11
whxiong@uestc.edu.cn NP theorem (3/7) NP Theorem: Likelihood ratio test (LRT) maximize PD for a given PFA =α , decide H1 if 11
NP theorem (3/7) NP Theorem:Likelihood ratio test(LRT) maximize PD for a given PEA=a,decide H if L)= P(x;H) P(x;Ho) whxiong@uestc.edu.cn
whxiong@uestc.edu.cn NP theorem (3/7) NP Theorem: Likelihood ratio test (LRT) maximize PD for a given PFA =α , decide H1 if L(x) = P(x; H1) P(x; H0) > °
NP theorem (3/7) NP Theorem:Likelihood ratio test(LRT) maximize Pp for a given PrA=a,decide H if P(x;H) P(x;Ho) The threshold y is determined from PEA as whxiong@uestc.edu.cn 13
whxiong@uestc.edu.cn NP theorem (3/7) NP Theorem: Likelihood ratio test (LRT) maximize PD for a given PFA =α , decide H1 if 13 L(x) = P(x; H1) P(x; H0) > ° The threshold γ is determined from PFA as
NP theorem (3/7) NP Theorem:Likelihood ratio test(LRT) maximize Pp for a given PEA=a,decide H if Zx)= P(x;Hi) P(x;Ho) The threshold y is determined from PrA as PFa-s p(x;Ho)dx a Lx):the likelihood ratio whxiong@uestc.edu.cn 14
whxiong@uestc.edu.cn NP theorem (3/7) NP Theorem: Likelihood ratio test (LRT) maximize PD for a given PFA =α , decide H1 if 14 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
NP theorem (3/7) NP Theorem:Likelihood ratio test(LRT) maximize Pp for a given PEA=a,decide H if 24x= P(x;Hi) P(x;Ho) The threshold y is determined from PrA as p(x;Ho)dx a L(x):the likelihood ratio Pu whxiong@uestc.edu.cn 15
whxiong@uestc.edu.cn NP theorem (3/7) NP Theorem: Likelihood ratio test (LRT) maximize PD for a given PFA =α , decide H1 if 15 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