model {
   alpha.star ~ dnorm(0.0,1.0E-4);     # intercept
   beta ~ dnorm(0.0,1.0E-4);      # mutagenic effect
   gamma ~ dnorm(0.0,1.0E-10);    # toxic effect
   tau ~ dpar(0.5, 0.04);         # Pareto prior on precision
   sigma <- 1.0/sqrt(tau);

   for(i in 1:doses){
      for(j in 1:plates){
         log(mu[i,j])   <- alpha.star + beta*(logx[i]-mean(logx[])) 
                           + gamma*(x[i]-mean(x[])) + lambda[i,j];
         y[i,j]          ~ dpois(mu[i,j]);
         lambda[i,j]     ~ dnorm(0.0,tau);
     }
     logx[i]        <- log(x[i]+10);
   }
   alpha <- alpha.star - beta*mean(logx[]) - gamma*mean(x[]);
}