I am not sure if I completely understand what lp_ is, I think it’s relative to log(joint density of auxiliry parameter and parameter theta), which is getting used in HMC to generate samples from the distribution. And I am not sure how to interpret the diagnostic results related to lp_, what it means when its Effective sample size ratio is lower than 0.2? Should we worry if that’s the only parameter whose Effective sample size ratio is below 0.5?
Roughly speaking, if I were enforced to choose a one-d summary of all possible univariate \hat R, I would probably choose lp__. In overparametrized models, it is often the other way around: the parameter inference may “get stuck” for weak identification, while lp__ looks fine. I am curious when lp__ is the only low ESS margin.