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In multiple sources a Gelman-Rubin MCMC convergence diagnostic of less than 1.1 is considered evidence that chains have converged.

For example in this thread:

https://stackoverflow.com/questions/54155673/is-there-a-function-check-rhat-in-rstan-package

I'm not clear why.

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Are you wondering how GR works, or why 1.1 seems to be the accepted cut-off. If the latter, you're not alone: arXiv paper questioning 1.1 cutoff argues that 1.1 is too high. They also propose a revised version of GR that is improved and can even evaluate a single chain.

The Stan folks are also working on a revised version of Stan's Rhat, which I believe is GR.

So if you're questioning 1.1, your instincts seem to be good. If you're questioning GR, the proposed revisions may also support your instincts.

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  • $\begingroup$ Thank you, it was the latter. $\endgroup$ – user3322865 Jul 10 at 19:34

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