The walk, seen on two of its coordinates · where it is ·
proposals it said no to · rings hold 50%, 90% and 99% of the target
Speed against acceptance rate · the limit, for any target ·
this step size, in the limit · this walk, measured
One coordinate over time, counted in units of d steps (the diffusion's clock)
The target is the standard Gaussian in d dimensions. From x the walk proposes y = x + (ℓ/√d) Z and moves there with
probability min(1, π(y)/π(x)); otherwise it stays. The limit is Roberts, Gelman and Gilks (1997): speed h = ℓ² · 2Φ(−ℓ/2),
highest at ℓ = 2.38, where 23.4% of proposals are accepted.