How does rjags process and update the input data in coda.samples()? - r

Question

I am working on a problem that requires me to use Metropolis Hastings algorithm to generate values for 3 unknowns, beta, lambda and phi for a group of users, and then use that output as an input for the gibbs sampler to solve a regression equation and further estimate the true values of beta, lambda and phi. I am using the rjags library in R, which works fine, but I don't clearly understand how the library is calculating the values under the hood.
The following is what the output of Metropolis Hastings looks like, let's say we did 3 iterations of MH, and had 3 users, so each user will have 3 values of beta, lambda and phi:
user number
beta
lambda
phi
1
0.1
0.2
0.5
1
0.2
0.2
0.3
1
0.1
0.4
0.3
2
0.8
0.4
0.6
2
0.7
0.5
0.7
2
0.8
0.4
0.7
3
1.8
2.4
1.7
3
3.6
4.8
6.1
3
3.6
8.2
3.2
I also have certain covariates for the 3 users:
user number
x1
x2
1
24
36
2
12
15
3
18
31
The above two tables go as input to rjags. Rjags code is as follows:
# metropolis is the output of MH
beta <- metropolis[,beta]
lambda <- metropolis[,lambda]
phi <- metropolis[,phi]
user_id <- metropolis[,user number
x1 <- covariates[, x1]
x2 <- covariates[, x2]
#number of MH iterations
N <- dim(metropolis)[1]
#number of customers
P <- metropolis[,uniqueN(user_id)]
data.jags <- list(beta = beta, lambda = lambda, phi = phi,
N = N, P = P,
user_id = user_id, x1 = x1, x2 = x2)
inits.jags <- list(".RNG.name" = "base::Wichmann-Hill",
".RNG.seed" = 111)
modelString <-
"model{
for (i in 1:N){
beta[i] ~ dnorm(theta_beta[cust_id[i]], tau_beta)
lambda[i] ~ dnorm(theta_lambda[cust_id[i]], tau_lambda)
phi[i] ~ dnorm(theta_phi[cust_id[i]], tau_phi)
}
for (j in 1:P){
theta_beta[j] <- d_0 + d_1 * x1 + d_2 * x2 + error_beta[j]
theta_lambdaj] <- g_0 + g_1 * x1 + g_2 * x2 + error_lambda[j]
theta_phij] <- e_0 + e_1 * x1 + e_2 * x2 + error_phi[j]
real_beta[j] <- exp(theta_beta[j])
real_lambda[j] <- exp(theta_lambda[j])/(1 + exp(theta_lambda[j]))
real_phi[j] <- exp(theta_phi[j])/(1 + exp(theta_phi[j]))
error_beta[j] ~ dnorm(0,0.1)
error_lambda[j] ~ dnorm(0,0.1)
error_phi[j] ~ dnorm(0,0.1)
}
#priors
d_0 ~ dnorm(0,0.01)
d_1 ~ dnorm(0,0.01)
d_2 ~ dnorm(0,0.01)
g_0 ~ dnorm(0,0.01)
g_1 ~ dnorm(0,0.01)
g_2 ~ dnorm(0,0.01)
e_0 ~ dnorm(0,0.01)
e_1 ~ dnorm(0,0.01)
e_2 ~ dnorm(0,0.01)
sigma_beta ~ dunif(0,100)
sigma_lambda ~ dunif(0,100)
sigma_phi ~ dunif(0,100)
tau_beta <- 1/pow(sigma_beta,2)
tau_phi <- 1/pow(sigma_phi,2)
tau_lambda <- 1/pow(sigma_lambda,2)
}"
Now, the results from the above code look fine, but I don't understand how exactly is the output of Metropolis Hastings (beta, lambda, phi) being used here. In the first for loop of the modelString, the values of beta, lambda and phi are being drawn from a normal distribution, so where do the values of beta, lambda and phi, which were given as inputs in data.jags come into picture?
Any kind of explanation/ insight would be much appreciated. Thanks!