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.

Cheers,

Arthus

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?