Rhat for deterministic quantities

Hi everyone and thanks for the great package with awesome support!

I have a question regarding the Rhat diagnostics. I followed the recently introduced HSGP approach and when I run model I get quite good values (about 1.03) for the linear coefficients (often called beta). However, in my setting the observed values are non-linearly related to the underlying GP and Rhat goes up to about 1.15 for one class of observations. These are deterministically related to the betas, so I wonder if this rise in Rhat is something to worry about or whether it’s expected.


I would consider that something to worry about and investigate it further. You might want to check a plot_rank of the problematic variable for example.

Rhat diagnostic is basically a comparison of within and between chain variances. If all chains are sampling the same distribution (which is the case if the MCMC has converged), it will necessarily be close to 1 as within and between chain variances will be the same. If there are convergence issues, chains might have different variances as they aren’t (yet) sampling from the MCMC target distribution.

A deterministic transformation which is applied to all chains cannot make the different chains represent different distributions if they were originally all samples of the same distribution. What is possible is that the transformation in question is ill-conditioned and makes small differences much more noticeable. This you might be able to see with the extra investigation (i.e. a 1.03 on the original variables translates to 1.15, and a 1.02 to 1.08, something like that)

Thank you for the kind and quick response. I checked the rank plots but didn’t see too much deviation from uniformity, much less than in the example over at rank_plot.

Are there other tricks to narrow down the issue? From looking around, the usual answer seems to be “reparametrize the model”, but I figure as the HSGP is basically a linear model it doesn’t get much simpler…and there is no way to reformulate the non-linear relation…What do you mean by the “(yet)” above? Should I maybe consider a longer tune-in phase?