Dear all,
I generated a hierarchical model data X by using some parameter true \theta^* then I fitted pystan on a hierarchical model using the generated data X.
I initialized the starting param (\theta_{stan}) to be the true parameter \theta^*, but the pystan model is having hard time in reaching the convergence, after I increase maximum_tree_depth (to 20)and adapt_detla(to 0.99) I had the parameter converging to some wrong value \theta_{stan}.
When I calculate the log_prob by using the fit.log_prob() function, I found the true param \theta^* indeeds have higher log prob but still the model converges to a way lower log prob param \theta_{stan}
Isn’t that wired that the stan is trying so hard (with 0.99 adapt_delta, 20 maximum tree depth) to reach a set of param \theta_{stan} that contains way lower log_prob? I understand from the previous post that those two sets of param \theta_{stan} and \theta^* should not be identical but close, however, now I am having two sets of param that are significantly different in terms of their log_prob evaluated.