#Bayesian robust MAP analysis with piecewise constant baseline hazard and 
#informative multivariate normal prior for alpha (baseline hazard) and 
#tau (precision of between-trial heterogeneity)
model {  
 ## Likelihoods ##
    for (i in 1:N) {
		      # define the likelihood
  			  mu[i] <- TimeIntervals[i]*exp(alpha[Interval[i]]+inprod(par[],X[i,])+theta[Trial[i]])
		  	  EventsIntervals[i] ~ dpois(mu[i]);
	   }
  
  #Informative multivariate normal prior on alpha, tau and par (covariate effects),
  #with reduced precision for robust component
  component ~ dcat(component_sizes)
	alpha ~ dmnorm(mean,precision_matrix[1:(K+1+P),1:(K+1+P),component]);
  tau <- exp(alpha[K+1]);

  #Theta's (trial specific effects) are normally distributed. 
  #Here we set the population mean of the theta's to zero,
  #because the alpha's already describe the baseline hazard.
    for (i in minTrial:maxTrial){
      theta[i] ~ dnorm(0, tau)
    } 
	#Normal prior on parameters
	 for (j in 1:P){
		 par[j] <- alpha[K+1+j];
	 }
}