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Specifically for the Stan implementation of HMC you can expect for most well-parameterized models to get more than one effective sample per 10 iterations. So the 10% threshold is a good one. If you’re getting fewer than that you should consider other options for parameterization (unless you’re getting a big enough effective sample size anyway, in that case carry on).
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I think it’s either close or already possible, not sure if it’s made it into the interfaces yet. It’s not much help though.
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Nah, if your sample is big enough and you meet the convergence criteria don’t worry about it. OTOH if you’re running Stan for hours/days to get your samples you are a) wasting your time; and b) likely using a terrible parameterization (or a very hard model) and you could do much better.
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All that stuff about running a million iterations and thinning by 10k is irrelevant for Stan/HMC, don’t do that.
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