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,

  • $\begingroup$ 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. $\endgroup$ – duckmayr Apr 23 '19 at 1:30

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