Deviance information criterion

The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation. Like AIC and BIC, DIC is an asymptotic approximation as the sample size becomes large. It is only valid when the posterior distribution is approximately multivariate normal.

Define the deviance as ${\displaystyle D(\theta )=-2\log(p(y|\theta ))+C\,}$, where ${\displaystyle y\,}$ are the data, ${\displaystyle \theta \,}$ are the unknown parameters of the model and ${\displaystyle p(y|\theta )\,}$ is the likelihood function. ${\displaystyle C\,}$ is a constant that cancels out in all calculations that compare different models, and which therefore does not need to be known.

...
Wikipedia