Deviance information criterion DIC

From https://en.wikipedia.org/wiki/Deviance_information_criterion : 

There are two calculations in common usage for the effective number of parameters of the model. The first, as described in Spiegelhalter et al. (2002, p. 587), is ${\displaystyle p_{D}={\overline {D(\theta )}}-D({\bar {\theta }})}$, where ${\displaystyle {\bar {\theta }}}$ is the expectation of ${\displaystyle \theta }$. The second, as described in Gelman et al. (2004, p. 182), is ${\displaystyle p_{D}=p_{V}={\frac {1}{2}}{\overline {\operatorname {var} \left(D(\theta )\right)}}}$. The larger the effective number of parameters is, the easier it is for the model to fit the data, and so the deviance needs to be penalized.

The deviance information criterion is calculated as

${\displaystyle \mathrm {DIC} =p_{D}+{\overline {D(\theta )}},}$

or equivalently as

${\displaystyle \mathrm {DIC} =D({\bar {\theta }})+2p_{D}.}$

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