I just constructed a Bayesian Hierarchical Model for my response variable Y that follows Poisson distribution with the parameter $\lambda$.
In my model, I have modelled $log(\lambda)$ as a linear function of 9 $\beta$'s and the covariate $X$, and I have assumed that the 9 $\beta$'s follow a multivariate normal distribution. In this case, is it okay to use Deviance Information Criterion (DIC) to compare this model with other models? I am asking this because someone told me that the DIC is not very reliable unless the Posterior is symmetric (e.g. normal distribution).