Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 36 / 3 / a / 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,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.