"mk" autocorrelation calculation about zeus HOT 4 OPEN

Hi @grahamgower,

Thanks for your comment.

I think I agree with what you say about the "MK" recipe although I believe the effect is very minor. I haven't seen a case in which it actually affects the outcome. Please let me know if you can think of anything where this could be a problem. A nice property of this estimator, apart from its lower variance (see the figure), is that it can help diagnose violations of ergodicity. E.g. If the walkers are unable to jump from mode to mode in a multimodal case the the MK estimate of the autocorrelation time would be equal to the length of the chain.

I've tried what you suggested and it seems to give similar results to the Goodman-Weare estimator as you can see in the figure bellow:

from zeus.

Thanks for your insights. I guess all these estimators are asymptotically unbiased when the chain length tends to inf.

I've tried what you suggested and it seems to give similar results to the Goodman-Weare estimator as you can see in the figure bellow:

Ah! This is obvious in hindsight because the fourier transform preserves linearity. Sorry, I should admit that I haven't looked at a fourier transform in quite some years (and never used one outside a classroom).

from zeus.

Here's another simple alternative that seems reasonable: https://arxiv.org/abs/2009.01799. They just take the ACvF of mean-centered chains, where the mean is calculated globally over all chains.

from zeus.

Thanks! That looks interesting, I'll have a look.

I'm not 100% sure that this applies to chains like the ones that zeus generates (from interacting walkers) but I'll have to read the paper first.

from zeus.