#  Cadralazine 2  (lognormal likelihood) ;
model {
	# N = total number of observations ;
	# n = number of patients ;
	# data transformation ;
		for (i in 1:N) {
		     lnconc[i] <- log(conc[i] + eps) ;  
                     # Adding eps prevents a trap because of 0-valed concs ;
		}
		# likelihood ;
		for (i in 1:N) {
		  	mu[i]  <- log(dose[i]) - ke[subj[i]] * time[i] - 
                            alpha[subj[i],1]
		      lnconc[i] ~ dnorm(mu[i], tauC)
			}
		# transformations of individual parameters  and 
                # second stage of model ;	
		for (i in 1:n) {
			V[i] <- exp(alpha[i,1]) ;
			ke[i] <- exp(alpha[i,2]) ;
			alpha[i,1:2] ~ dmnorm(eta[1:2], tau[1:2, 1:2])
		}
		# transformations of population parameters priors ;
		eta[1:2] ~ dmnorm(mean[1:2], prec[1:2, 1:2])
		tau[1:2, 1:2] ~ dwish(R[1:2, 1:2], 2)
		Vpop <- exp(eta[1]) ;
		kepop <- exp(eta[2]) ;
		
	 for (i in 1:2) { 
		sigma[i] <- sqrt(inverse(tau[1:2, 1:2], i, i))
		 }

		tauC ~ dgamma(1.0E-3, 1.0E-3)
		sigmaC <- 1 / sqrt(tauC)	
	}
	
	data
	list(N = 64, n = 10, mean = c(0, 0), eps = 0.000001, 
			R = structure(.Data = c(0.1, 0, 
													0, 0.1), .Dim = c(2,2)),
			prec = structure(.Data = c(1.0E-6, 0, 
													0, 1.0E-6), .Dim = c(2,2)))
													


		
inits
list(eta = c(0,0), tauC = 2.0, tau = structure(.Data =
c(0.1, 0.0, 0.0, 0.1), .Dim = c(2,2)) )

list(eta = c(2.5,  -2.5), tauC = 1.0, tau = structure(.Data =
c(25.0, 5.0, 5.0, 25.0), .Dim = c(2,2)) )

list(eta = c(-2.5, 2.5), tauC = 0.5, tau = structure(.Data =
c(1,0,0,1), .Dim = c(2,2)) )