[R] Calculating DIC from MCMC output

[Kyle Edwards]

Greetings all,

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