denogi_dyn.bug

model{
    for (i in 1:N){
        for (t in 1:T){
            for (j in 1:K){
                mu[t, j, i] <- beta[j, 1] + beta[j, 2]*x[t, i]
                y[t, j, i] ~ dnorm(mu[t, j, i], tau[j])
            }
        }
    }

    # transition
    for (i in 1:N){
        for (t in 2:T){
            mu_x[t, i] <- gamma[1] + gamma[2]*x[t - 1, i]
            x[t, i] ~ dnorm(mu_x[t, i], prec_sigma_x)
        }
    }
    for (i in 1:N){
        x[1, i] ~ dnorm(0, 0.0001) # initialisation
    }

    # priors
    sigma_x ~ dunif(0, drift)
    prec_sigma_x <- pow(sigma_x, -2)
    gamma[1:2] ~ dmnorm(g0, G0)

    for (j in 1:K){
        beta[j, 1:2] ~ dmnorm(g0, G0)
        tau[j] ~ dgamma(0.01, 0.01)
        omega[j] <- 1/sqrt(tau[j])
    }

    # remapping
    sd_x <- sd(x)
    mean_x <- mean(x)
    for (i in 1:N){
        for (t in 1:T){
            country[t, i] <- (x[t, i] - mean_x) / sd_x
        }
    }
    for (j in 1:K){
        load[j] <- beta[j, 2] * sd_x
        intercept[j] <- beta[j, 1] + beta[j, 2]*mean_x/sd_x
    }
}