The limiting diffusion approximation admits a straightforward efﬁ-No one breaks it down for the layperson like a statistician!

ciency maximization problem, and the resulting asymptotically optimal

policy is related to the asymptotic acceptance rate of proposed moves for

the algorithm. The asymptotically optimal acceptance rate is 0.234 under

quite general conditions.

Supposedly ~50% is optimal for problems with 1 or 2 parameters (Section 4.2 of Gregory 2005). But if you have only 1 or 2 parameters, I don't know why you'd want to do MCMC, unless there is a nonanalytic likelihood to evaluate through a simulation or something. Gregory cites Roberts et al. above, but I didn't see anything about 50% for simpler problems. If you decide to read Roberts et al., let me know if I missed the note about 50%.

That said, 30-40% has treated me well over the years. Let's say you should aim for 25-30% acceptance of your jump proposals for the full line profile fit (Problem 3 of CA6).

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