MODEL:
Y=a*T1*P1*W*E*P2/(1+P2/b)+c*T2+d
Input data：
T1= [0.9902 0.9696 0.9851 0.9341 0.9787 0.9502 0.8941 0.9987 0.9987 0.9897 0.9946 0.7887]
T2= [18.261 22.945 22.074 24.285 22.474 23.742 25.379 20.631 19.377 21.735 18.711 11.493]
P1= [0.5961 0.5777 0.5989 0.6213 0.6258 0.6478 0.6416 0.6554 0.6514 0.6553 1.0000 1.0000]
P2= [19265.5 18877 18052.5 15476 20851.5 21657 22012 6481 21738 20884 17597.5 18969]
W= [0.8755 0.8492 0.8791 0.9119 0.9176 0.9511 0.9417 0.9625 0.9552 0.9615 0.9525 0.9180]
E= [0.2927 0.2817 0.3708 0.4006 0.3684 0.4377 0.4311 0.4939 0.4847 0.4762 0.4602 0.4043]
Yo= [-6.23 -7.24 2.21 6.1 15.18 16.38 13.63 2.53 10.51 4.08 0.73 3.51]
Cost function:
J(p) = 1/2*[(Yo-Y(p))'Co ^(-1) (Yo-Y(p))+(p-pb) ' Pb^(-1) (p-pb)]
where Yo represents the data vector, Y(p) is the model output vector, Co and Pb the error covariance matrix on data and model parameters, respectively. p is the parameter vector. pb is a priori values of p.
pb = [0.06, 1600, 0.05, 1];
My question is how to estimate the parameter (a, b, c, d) using WinBUGS?
Y=a*T1*P1*W*E*P2/(1+P2/b)+c*T2+d
Input data：
T1= [0.9902 0.9696 0.9851 0.9341 0.9787 0.9502 0.8941 0.9987 0.9987 0.9897 0.9946 0.7887]
T2= [18.261 22.945 22.074 24.285 22.474 23.742 25.379 20.631 19.377 21.735 18.711 11.493]
P1= [0.5961 0.5777 0.5989 0.6213 0.6258 0.6478 0.6416 0.6554 0.6514 0.6553 1.0000 1.0000]
P2= [19265.5 18877 18052.5 15476 20851.5 21657 22012 6481 21738 20884 17597.5 18969]
W= [0.8755 0.8492 0.8791 0.9119 0.9176 0.9511 0.9417 0.9625 0.9552 0.9615 0.9525 0.9180]
E= [0.2927 0.2817 0.3708 0.4006 0.3684 0.4377 0.4311 0.4939 0.4847 0.4762 0.4602 0.4043]
Yo= [-6.23 -7.24 2.21 6.1 15.18 16.38 13.63 2.53 10.51 4.08 0.73 3.51]
Cost function:
J(p) = 1/2*[(Yo-Y(p))'Co ^(-1) (Yo-Y(p))+(p-pb) ' Pb^(-1) (p-pb)]
where Yo represents the data vector, Y(p) is the model output vector, Co and Pb the error covariance matrix on data and model parameters, respectively. p is the parameter vector. pb is a priori values of p.
pb = [0.06, 1600, 0.05, 1];
My question is how to estimate the parameter (a, b, c, d) using WinBUGS?
