Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 219 / 2 / b

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- Solution b

Solution

The simulation catalog is a sample from the joint prior. Self-normalized importance sampling therefore estimates the posterior mean by

\overline{m}_{w} = \sum_{i = 1}^{K} m_{i} w_{i}, w_{i} = \frac{p ( d ∣ x _{i} )}{\sum _{j = 1}^{K} p ( d ∣ x _{j} )} .

The likelihood weights update each simulated system according to how well its satellite resembles the measured one.

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