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Dear Margaret,

The var(deviance)/2 formula used by the R2jags package has been around a
long time. You can see a discussion of it from 2006 in Andrew Gelman's
blog, including a rationale for why it was included in the R2WinBUGS
package.

http://andrewgelman.com/2006/07/06/number_of_param/

Thanks to Sumio Watanabe, we now know that the correct penalty is based
on the sum of the variances of the individual contributions to the
deviance and not the variance of the sum. This gives the "widely
applicable information criterion", or WAIC. So the formula used in the
R2jags package is "close, but no cigar".

I wrote JAGS but not the R2jags package. I can't take any credit for
R2jags so please be careful with your attributions. The native interface
between R and JAGS is the rjags package and this gives you access to DIC
statistics via the dic.samples() function. At the risk of muddying the
waters further, this uses a third definition of pD which, nevertheless,
has some justification. See the references on the help page for
dic.samples. 

regards
Martyn

On Thu, 2015-09-03 at 15:41 +1000, Margaret Donald wrote:
> Dear Gibbs samplers,
> 
> 
> Does anyone have a reference which gives the reason for the definition
> of pD in JAGS as deviance/2, versus the Spiegelhalter et al (2002)
> definition as pD= Bbar-Dhat.
> 
> 
> I have been struggling to initialize 3 chains in Brugs and have been
> working in R2jags where parameter initilization ise easier, but I am
> surprised and not happy with JAGS' pD  (different) definition..  So
> far I have not discovered the rationale...
> 
> 
> Some thoughts would be most welcome.
> 
> 
> Regards,
> Margaret Donald
> 
> 
> -- 
> Margaret Donald
> Post Doctoral researcher
> University of New South Wales
> [log in to unmask]
> 0405 834 550


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