= Bayesian deviance
{c}
{title2=$D(\theta)=-2\log L(\theta)$}
A <Bayesian deviance> is minus twice the <log-likelihood>, with any chosen additive data-only constant held consistent across the models being compared. Its <Bayesian posterior> expectation measures average fit. In the <deviance information criterion>, evaluating it at a parameter's <posterior mean> also enters the effective complexity penalty. This likelihood-based convention differs by a data-only constant from a saturated-model <exponential-family deviance> when a common saturated model exists.
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