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Hi All:

I was looking for some help to code an equation of ellipse within WinBUGS.
I need to form a Bivariate ellipse using p1's in my data. I tried to use
the equation as (X-mu)'*sigmainverse*(X-mu), where X is the Bivariate
Normal Variable, mu is the vector of means and sigmainverse is the inverse
of the var-covariance matrix. In my example p1's are Bivariate Normal
Variables with mean gamma and inverse sigma2 matrix. Highlighted below is
what I did but it doesnot work. Heres the WinBUGS code:
model
 {
  for (j in 1 : Nf)

      {
      p1[j, 1:2 ] ~ dmnorm(gamma[1:2 ], T[1:2 ,1:2 ])
 # gamma is the MVN mean or mean of logit (p)
#T is the precision matrix inverse sigma of MVN or logit(p)
# precision equals reciprocal of variance
# precision matrix is the matrix inverse of the covariance matrix
      for (i in 1:2)
      {
     logit(p[j,i])<-p1[j,i]

     Y[j,i] ~ dbin(p[j,i],n)

     wp[j,i] <- p[j,i]*dbw[j,i]
     }

     sumwp[j] <- sum(wp[j, ])
ell[j]<-((t(p1[j,1:2]-gamma[1:2]))*T[1:2,1:2]*(p1[j.1:2]-gamma[1:2]))
      }

     # Hyper-priors:

     gamma[1:2] ~ dmnorm(mn[1:2],prec[1:2 ,1:2])
expit[1]<-exp(gamma[1])/(1+exp(gamma[1]))
expit[2]<-exp(gamma[2])/(1+exp(gamma[2]))
      T[1:2 ,1:2] ~ dwish(R[1:2 ,1:2], 2)
     sigma2[1:2, 1:2] <-inverse(T[,])
#sigma2 is the covariance matrix
     rho <- sigma2[1,2]/sqrt(sigma2[1,1]*sigma2[2,2])
#rho is the correlation matrix

     }
expit[i]<-exp(gamma[i])/(1+exp(gamma[i]))
}

     # Data
     list(Nf =20, mn=c(-0.69, -1.06), n=60,
     prec = structure(.Data = c(.001, 0,
                    0, .001),.Dim = c(2, 2)),
     R = structure(.Data = c(.001, 0,
                 0, .001),.Dim = c(2, 2)),
     Y= structure(.Data=c(32,13,
                 32,12,
                 10,4,
 28,11,
 10,5,
 25,10,
  4,1,
 16,5,
 28,10,
 21,7,
 19,9,
 18,12,
 31,12,
 13,3,
 10,4,
 18,7,
 3,2,
 27,5,
 8,1,
 8,4),.Dim = c(20, 2)),
dbw=structure(.Data=c(0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25,
0.25,0.25),.Dim=c(20,2))
)

Thanks
Anamika

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