Bayesian Approach 。PDFS pA)= daw{-2不4 p(A)Prob(A<-A1)6(A+A0) + Pa(A,A)u(+Ao)-u(A-Ao) +Prob(A>Ao)6(A-Ao)》 A-A刘Paa>a-4paa 10 whxiong@uestc.edu.cn 11
whxiong@uestc.edu.cn PDFs Bayesian Approach 11 p(A b ) = 1 (2¼¾2 =N) 1 2 ¢exp ½ ¡ 1 2¾2 =N (A b ¡ A) ¾ p(A¸) = Prob(A· < ¡A1)±(A· + A0) + PAb (Ab; A) h u(A¸ + A0) ¡ u(A¸¡ A0) i + Prob(A¸ > A0)±(A¸¡ A0) Z ¡A0 ¡1 (A b ¡ A) 2 PA b (A b ; A)dA b > (A0 ¡ A) 2 Z ¡A0 ¡1 PA b (A b ; A)dA b
Bayesian Approach 。PDFS pA)= m{-2不-4刘 p(A)Prob(A<-A1)6(A+A0) + PaA,A)u(A+A)-以i-A) +Prob(A>Ao)6(A-Ao)》 f 10 (A-A)Pa(AA)dA>(Ao-A)2Pa(A)da MSE(A>MSE(A) whxiong@uestc.edu.cn 12
whxiong@uestc.edu.cn PDFs Bayesian Approach 12 p(A b ) = 1 (2¼¾2 =N) 1 2 ¢exp ½ ¡ 1 2¾2 =N (A b ¡ A) ¾ p(A¸) = Prob(A· < ¡A1)±(A· + A0) + PAb (Ab; A) h u(A¸ + A0) ¡ u(A¸¡ A0) i + Prob(A¸ > A0)±(A¸¡ A0) Z ¡A0 ¡1 (A b ¡ A) 2 PA b (A b ; A)dA b > (A0 ¡ A) 2 Z ¡A0 ¡1 PA b (A b ; A)dA b MSE(A b ) > MSE(A ¸ )
Bayesian Approach Unknowns A is deterministic minimize MSE MSE(A(A-A)"p(x;A)dx whxiong@uestc.edu.cn 13
whxiong@uestc.edu.cn Unknowns A is deterministic minimize MSE Bayesian Approach 13 MSE(A b ) = Z (A b ¡ A) 2 p(x; A)dx
Bayesian Approach Unknowns A is deterministic>minimize MSE MSE(A(A-A)p(x:A)dx Unknowns is RV>minimize mean MSE whxiong@uestc.edu.cn 14
whxiong@uestc.edu.cn Unknowns A is deterministic minimize MSE Bayesian Approach 14 MSE(A b ) = Z (A b ¡ A) 2 p(x; A)dx Unknowns is RV minimize mean MSE
Bayesian Approach Unknowns A is deterministic>minimize MSE MSE(④=a-APp6xAdk Unknowns is RV->minimize mean MSE BMsE(A(A-A)p(x,A)dixdA whxiong@uestc.edu.cn 15
whxiong@uestc.edu.cn Unknowns A is deterministic minimize MSE Bayesian Approach 15 MSE(A b ) = Z (A b ¡ A) 2 p(x; A)dx Unknowns is RV minimize mean MSE BMSE(A b ) = Z Z (A ¡ A b ) 2 p(x; A)dxdA