Prior on beta in log logistic AFT model 

model{
  for(i in 1:r){
    w[i] ~ dlogis(mu0[i],tautilde0[i])
    mtilde[i] <- exp(w[i]) # So mtilde[i] ~ Log-Logistic
    mu0[i] <- log(mtilde0[i])
    tautilde0[i] <- 1/sigmatilde0[i]
    lmtilde[i] <- log(mtilde[i])
    beta[i] <- inprod(Xtildeinv[i,1:r], lmtilde[1:r])
  }
}
list(r =2, mtilde0 = c(10,20), sigmatilde0 = c(2,2))  #  These aren't the correct values for sigmatilde0.  Used here for convenience.
# The matrix Xtildeinv = solve(Xtilde) was obtained in R
Xtildeinv[,1]   Xtildeinv[,2]  
1          0
-0.5   0.5
END

 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	beta[1]	2.3	3.631	0.01512	-5.087	2.3	9.619	1	50000
	beta[2]	0.3578	2.579	0.01053	-4.787	0.363	5.47	1	50000

 

Prior on beta in Weibull AFT model 

model{
  for(i in 1:r){
    mtilde[i] ~ dweib(alphatilde0[i],thetatilde0[i])
    thetatilde0[i] <- log(2)*exp(-mu0[i]*sqrt(tautilde0[i]))
    alphatilde0[i] <- sqrt(tautilde0[i])
    mu0[i] <- log(mtilde0[i])
    tautilde0[i] <- 1/pow(sigmatilde0[i],2)
    lmtilde[i] <- log(mtilde[i])
    beta[i] <- inprod(Xtildeinv[i,1:r], lmtilde[1:r])
  }
}
list(r =2, mtilde0 = c(10,20), sigmatilde0 = c(2,2))  #  These aren't the correct values for sigmatilde0.  Used here for convenience.
# The matrix Xtildeinv = solve(Xtilde) was obtained in R
Xtildeinv[,1]   Xtildeinv[,2]  
1          0
-0.5   0.5
END

 	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	beta[1]	1.882	2.559	0.01084	-4.303	2.305	5.663	1	50000
	beta[2]	0.3376	1.821	0.007548	-3.322	0.3354	4.014	1	50000

model{
  for(i in 1:r){
    mtilde[i] ~ dlnorm(mu0[i],tautilde0[i]) # mtilde[i] ~ LN
    mu0[i] <- log(mtilde0[i]) # Prior guess is mtilde0[i]
    tautilde0[i] <- 1/pow(sigmatilde0[i],2)
    lmtilde[i] <- log(mtilde[i])
    beta[i] <- inprod(Xtildeinv[i,1:r] , lmtilde[1:r])
  }
Xtildeinv[1:2,1:2] <- inverse(Xtilde[1:2,1:2])
a ~ dbern(1)
b[1] <- a*Xtildeinv[1,1]
b[2] <- a*Xtildeinv[1,2]
b[3] <- a*Xtildeinv[2,1]
b[4] <- a*Xtildeinv[2,2]
}
list(r =2, mtilde0 = c(10,20), sigmatilde0 = c(2,2))  #  These aren't the correct values for sigmatilde0.  Used here for convenience.
Xtilde[,1]   Xtilde[,2]
1 0
1 2
END

model{
  for(i in 1:r){
    mtilde[i] ~ dlnorm(mu0[i],tautilde0[i]) # mtilde[i] ~ LN
    mu0[i] <- log(mtilde0[i]) # Prior guess is mtilde0[i]
    tautilde0[i] <- 1/pow(sigmatilde0[i],2)
    lmtilde[i] <- log(mtilde[i])
    beta[i] <- inprod(Xtildeinv[i,1:r] , lmtilde[1:r])
  }
}
list(r =2, mtilde0 = c(10,20), sigmatilde0 = c(2,2))  #  These aren't the correct values for sigmatilde0.  Used here for convenience.
Xtildeinv[,1]   Xtildeinv[,2]
1 0
0 0.5
END

model{
Xtildeinv[1:2,1:2] <- inverse(Xtilde[1:2,1:2])
a ~ dbern(1)
b[1] <- a*Xtildeinv[1,1]
b[2] <- a*Xtildeinv[1,2]
b[3] <- a*Xtildeinv[2,1]
b[4] <- a*Xtildeinv[2,2]
}
Xtilde[,1]   Xtilde[,2]
4 3
1 2
END

model{
Xtildeinv[1:2,1:2] <- inverse(Xtilde[1:2,1:2])
a ~ dbern(1)
b[1] <- a*Xtildeinv[1,1]
b[2] <- a*Xtildeinv[1,2]
b[3] <- a*Xtildeinv[2,1]
b[4] <- a*Xtildeinv[2,2]
}
Xtilde[,1]   Xtilde[,2]
4 2
2 4
END