Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 219 / 3 / e / Solution

The light-curve posterior used the analysis prior ${\pi }_0(\Delta t)=N(0,{\sigma }_{\mathrm{prior}}^2)$, so its marginal likelihood as a function of delay is proportional to $p(\Delta t\mid D)/{\pi }_0(\Delta t)$. ThereforeThe integral can be evaluated numerically using the approximation from part (d).