model
{
for (s in 1 : regions) {
for (t in 1 : time) {
#Negative binomial likelihood for observed counts
cases[s,t] ~ dnegbin(p[s,t],kappa)
p[s,t]<-kappa/(kappa+mu[s,t])
log(mu[s,t]) <- log(e[s,t])+alpha+beta1*x1[s,t]+beta2*x2[s,t]+beta3*x3[t]
+gamma1*w1[s]+gamma2*w2[s,t]+delta*z[s,t]+phi[s]+nu[s]+omega[month[t]]
}
#Prior distributions for the uncorrelated heterogeneity
phi[s] ~dnorm(0,tau.phi)
}
#CAR prior distribution for the spatially correlated heterogeneity
nu[1:regions] ~car.normal(adj[], weights[], num[], tau.nu)
for(k in 1:sumNumNeigh) {
weights[k] <- 1
}
#Prior distribution for the scale parameter
kappa~dgamma(0.5,0.0005)
#Improper uniform prior distribution for the intercept
alpha ~ dflat()
#Prior distributions for the autocorrelated month effect (annual cycle)
omega[1]<-0
for (i in 2:12)
{
omega[i] ~ dnorm(omega[i-1],tau.omega)
}
#Prior distributions for climate and non-climate covariates
beta1 ~ dnorm(0.0,1.0E-6)
beta2 ~ dnorm(0.0,1.0E-6)
beta3 ~dnorm(0.0,1.0E-6)
gamma1 ~dnorm(0.0,1.0E-6)
gamma2 ~ dnorm(0.0,1.0E-6)
delta ~ dnorm(0.0,1.0E-6)
#Hyperprior distributions on inverse variance parameter of random effects
tau.phi~dgamma(0.5, 0.0005)
tau.nu~dgamma(0.5, 0.0005)
tau.omega~dgamma(0.5, 0.0005)
}

list(e=structure(.Data=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4),.Dim=c(5,12)),cases=structure(.Data =c(1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01,     NA,     NA,     NA,     NA,     NA),.Dim = c(5,12)), x1=structure(.Data=c(1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01),.Dim = c(5,12)),x2=structure(.Data =c(1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01), .Dim = c(5,12)),x3=c(1,2,3,4,1,2,3,4,1,2,3,4),  w1=c(1.00000E+00, 2.00000E+00, 1.00000E+00, 1.00000E+00, 2.00000E+00),w2=structure(.Data =c(1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01),.Dim = c(5,12)),z=structure(.Data =c(1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 1.20000E+01, 1.10000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 2.30000E+01, 2.20000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01, 3.40000E+01, 3.30000E+01),.Dim = c(5,12)),regions=5,time=12,num=c(2,2,2,3,1),
adj=c(
2,4,
1,3,
2,4,
1,3,5,
4),
sumNumNeigh=10,month=c(1,2,3,4,5,6,7,8,9,10,11,12))


list(alpha=1,y[1,12]=44,y[1,12]=24,y[3,12]=24,y[4,12]=24,y[5,12]=24,beta1=1,beta2=1,gamma1=1)