NUTS does not converge in areas with high likelihood

Hi I am trying to use NUTS to sample poterior distribution of two hyperparameters for Gaussian Process Regression. I have two questions of it:

  1. How to get the log probability of samples with pyro? I found an answer for numpyro but that seems do not work for pyro.

  2. The results are shown in the figure below, it seems like the posterior samples does not converge in areas with high likelihood. I am wondering is it a nature bahabviour of NUTS or how can I improve it? Note, Empirical Bayes indicate the optimised hyperparameters by SVI.

i don’t recommend taking SVI as any kind of gold standard. also you’re generally providing too few details for your question to be actionable in any way, unfortunately.