Usually you can do the predictions in JAGS. Below is a regression example with FEV (something to do with lung capacity) as the dependent variable and age and smoking indicator as predictors.
FEV20s and FEV20ns are the predicted FEV values for a 20 year old smoker and a 20 year old non-smoker.
model
{
for(i in 1:n){
FEV[i] ~ dnorm(mu[i],tau)
mu[i] <- beta[1] + beta[2]*Age[i] + beta[3]*Smoke[i] + beta[4]*Age[i]*Smoke[i]
}
#priors
beta[1] ~ dnorm(0,0.001)
beta[2] ~ dnorm(0,0.001)
beta[3] ~ dnorm(0,0.001)
beta[4] ~ dnorm(0,0.001)
tau ~ dgamma(0.001,0.001)
sigma<-1/sqrt(tau)
## Predict the FEV for a 20 year old smoker and for a 20 year old nonsmoker
mu20s <- beta[1] + (beta[2]+beta[4])*20 + beta[3]
mu20ns <- beta[1] + beta[2]*20
FEV20s ~ dnorm(mu20s,tau)
FEV20ns ~ dnorm(mu20ns,tau)
}
Example from: Bayesian Ideas and Data Analysis