Discard burn-in from the MCMC output and retain the sampled $\Delta t$ coordinate. A normalized histogram or <kernel density estimation> of these draws approximates $p(\Delta t\mid D)$. Autocorrelation changes the Monte Carlo uncertainty, so uncertainty bands should use the chain's effective sample size rather than its raw length.

Solution

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

 Solution (source code)