# [R] Calculating DIC from MCMC output

From: Kyle Edwards <kedwards_at_ucdavis.edu>
Date: Tue 03 Apr 2007 - 02:07:51 GMT

I'm a newcomer to Bayesian stats, and I'm trying to calculate the Deviance Information Criterion "by hand" from some MCMC output. However, having consulted several sources, I am left confused as to the exact terms to use. The most common formula can be written as

DIC = 2*Mean(Deviance over the whole sampled posterior distribution)
- Deviance(Mean posterior parameter values)

However, I have also seen this as

DIC = 2*Mean(Deviance over the whole sampled posterior distribution)
- Min(Deviance over the whole sampled posterior)

Now, my understanding is that for some distributions, the deviance at the parameter means will be equal to the minimum deviance (i.e. these are the maximum likelihood parameter values). But, in other cases this will not be true. I have also read that the choice of exactly which point estimate of the parameters to use is somewhat arbitrary (i.e. one could use the mean, the mode, the median). It would be much easier for me to analyze this data if I can just use the formula with Min(Deviance). Could anyone comment on the difference between these and recommend the best course?

Thanks,

Kyle

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