= Solution
The logarithm is strictly increasing, so maximizing the <likelihood function> is equivalent to maximizing its logarithm. Multiplication by $-2$ reverses that ordering. Thus, whenever the maximum is attained,
$$
\boxed{\widehat\theta\in\operatorname*{arg\,max}_\theta p(y\mid\theta)
\quad\Longleftrightarrow\quad
\widehat\theta\in\operatorname*{arg\,min}_\theta D(\theta).}
$$
Here the <Bayesian deviance> includes the likelihood constants. Parameter-independent constants do not alter the minimizer, but a common convention must be retained when comparing criteria between models.
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