# Can Deviance Information Criterion be used for model comparison when the response variable has Poisson distribution?

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).

Thank you,

• It is true that extreme asymmetry can cause problems with DIC, but I have seen accepted work using DIC with Poisson distributed response variable; for example, this paper published in Political Analysis presenting a Bayesian Poisson Vector Autoregression model. – duckmayr Apr 23 at 1:30