var
   age[I],  year[I],   cases[I], pyr[I], mu[I], alpha[Nage],
   beta[K], betamean[K],  betaprec[K], logRR[K], tau, sigma;
model {
   for (i in 1:I) {
      cases[i]        ~ dpois(mu[i]);
      log(mu[i])     <- log(pyr[i]) + alpha[age[i]] + beta[year[i]]
   }

   betamean[1]    <- 0.0; 
   betaprec[1]    <- tau*1.0E-6; 
   betamean[2]    <- 0.0;  
   betaprec[2]    <- tau*1.0E-6; 
   for (k in 3:K){
      betamean[k]    <- 2*beta[k-1] - beta[k-2];
      betaprec[k]    <- tau 
   } 

   for (k in 1:K){
      beta[k]        ~ dnorm(betamean[k],betaprec[k]);
      logRR[k]      <- beta[k] - beta[5]
   }

   alpha[1]      <- 0.0;   
   for (j in 2:Nage){
      alpha[j]       ~ dnorm(0,1.0E-6)
   }
   sigma ~ dunif(0,1);
   tau   <- 1/(sigma*sigma);
}