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When to pick what, for this kind of problem
For a 3–6 parameter spectrum with a well-behaved posterior, like this one, the practical recommendation is:
- First fit: use nest with parallel nest 4 as the first-pass exploration. It gives you both the posterior and the evidence; the elapsed time is tolerable for everything up to about ten parameters with a moderate-binning response. (Goodman–Weare is the default sampler and is the lowest-friction choice for routine work — see the decision flow below — but on a short benchmark like this one its effective-sample yield per unit time is poor.)
- Refinement around a known mode: switch to chain type mh with the chain proposal gaussian fit proposal. It is cheap, converges quickly, and produces independent-looking samples without further tuning.
- Higher-dimensional problems (more than a dozen parameters), or models where the posterior has long correlated directions: switch to hmc, accept the higher per-sample cost, and budget for at least 1000 warmup samples per chain.
- Avoid Goodman–Weare for small-budget runs. It is excellent on long runs at high dimension where it can amortize the walker burn-in, but for short benchmarks like this one its ESS per sample is too low.