 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-219/3/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

With

D = (y_{1}, y_{2}, t)

and

ν = (Δ m, c, A, τ)

p (θ ∣ D) \propto p (y_{1}, y_{2} ∣ t, θ) exp (- \frac{Δ t ^{2}}{2 σ _{prior}^{2}}) p (ν) .

θ^{'} = θ + Z

from a symmetric multivariate normal increment, conveniently using logarithmic coordinates for

A, τ > 0

, and accepts with probability

min {1, \frac{p ( θ ^{'} ∣ D )}{p ( θ ∣ D )}} .

After burn-in, retain a suitably long chain and assess convergence and effective sample size of a Markov chain.

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