NP theorem (4/7) Question:Can we minimize PeA and 1-Po simultaneously? whxiong@uestc.edu.cn 16
whxiong@uestc.edu.cn NP theorem (4/7) Question: Can we minimize PFA and 1- PD simultaneously? 16
NP theorem (4/7) Question:Can we minimize PeA and 1-Pp simultaneously? Observations X H R Ho whxiong@uestc.edu.cn 17
whxiong@uestc.edu.cn NP theorem (4/7) Question: Can we minimize PFA and 1- PD simultaneously? 17 R0 R1 Observations X H0 H1
NP theorem (4/7) Question:Can we minimize PeA and 1-Pp simultaneously? Observations X p(x;Ho)dx Ro PD=p(x:H1)dx x∈R1 Ho whxiong@uestc.edu.cn 18
whxiong@uestc.edu.cn NP theorem (4/7) Question: Can we minimize PFA and 1- PD simultaneously? 18 R0 R1 Observations X H0 H1 PFA = Z x2R1 p(x; H0)dx PD = Z x2R1 p(x; H1)dx
NP theorem (4/7) Question:Can we minimize PeA and 1-Pp simultaneously? Observations X H p(x;Ho)dx Ro p(x;H1)dx Ho p(X:Hy)is positive,thus Larger region(e.g.,R)means larger integral>PEA and Pp have same trend whxiong@uestc.edu.cn 19
whxiong@uestc.edu.cn NP theorem (4/7) Question: Can we minimize PFA and 1- PD simultaneously? 19 R0 R1 Observations X H0 H1 PFA = Z x2R1 p(x; H0)dx PD = Z x2R1 p(x; H1)dx p(X; HX ) is positive, thus Larger region (e.g., R1 ) means larger integralPFA and PD have same trend