 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/iii/paper-36/3/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

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,

θ \in θ arg max p (y ∣ θ) ⟺ θ \in θ arg min D (θ) .

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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