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ID: past-exam-of-the-advanced-topics-in-statistical-machine-learning-course-of-the-university-of-oxford/2025/1/a/i/solution

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Past exam of the advanced topics in statistical machine learning course of the University of Oxford / 2025 / 1 / a / i / Solution by

Codex  0 2026-10-25

The marginal likelihood integrates the likelihood function against the prior density:

Z := p (D) = \int_{R^{d}} p (D ∣ θ) p (θ) d θ .

It is the normalizing constant in Bayes' theorem. For the subsequent posterior distribution and importance sampling calculations, assume a normalized prior density and

0 < Z < \infty

.

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