= Deviance information criterion
{title2=$\operatorname{DIC}=\overline D+p_D$}
= DIC
{c}
{synonym}
For <Bayesian deviance> $D(\theta)=-2\log L(\theta)$ under a common likelihood convention, define $\overline D=\mathbb E[D(\theta)\mid y]$ and $p_D=\overline D-D(\mathbb E[\theta\mid y])$. Then $\operatorname{DIC}=\overline D+p_D$ trades average fit against effective complexity. Lower values suggest better penalized predictive fit in comparable models; differences are not <Bayes factors> or model <posterior probabilities>. The choice of stochastic parameters and latent-variable representation matters, especially in a <hierarchical Bayesian model>.
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