Divergent transitions after warm up & Rhat


#1

After I fitting my model, there is a warning of 10 divergent transitions after warm up. However, the Rhat is 1 for all parameters. Should Rhat be an indicator of divergence?

Thanks!


#2

No. Divergent transitions are an indicator of parts of the parameter space that the sampler cannot get to. Rhat just tells you that the chains have similar means.


#3

Thank you so much. Now the terms are much more clear to me:)


#4

Divergences are when Stan can’t follow the Hamiltonian trajectory—the Hamiltonian, which should remain constant, diverges. As @bgoodri says, R-hat just measures that the within-chain means and variances match the cross-chain means and variances. It’s possible for draws to have decent looking R-hat when chains have not fully explored the posterior. Divergences are an additional way of signaling that something may be going wrong.

If you only have a few, increase adapt_delta and potentially lower stepsize (the latter is just the init value, so it’s not as critical if you’re converging to the typical set in all chains already).


#5

Importantly, divergences are a more sensitive diagnostics than R-hat, so often you’ll see indications of problems from non-zero divergences before they manifest as bad R-hats amongst different chains.

For more on how to use divergences see http://mc-stan.org/users/documentation/case-studies/divergences_and_bias.html.


#6

Thank you all for the thorough explanations.