This is a general question, not strictly about a specific Stan model. (But it’s a spin-off question from this).
Can it be that if I’m dealing with an unidentified complex model, I get biased posterior distributions? That is, I generate data with known true values for the parameters and I get (too) precise 95% CrI that exclude the true values? (Or does this mean that I have an error somewhere else in the model?)
I understand that the most common scenario would be that the model doesn’t converge because the posteriors have many modes and the chains get stuck in different modes. Or if I have good priors then the posteriors of the unidentified model would be more or less the priors. But I faced this problem of biased posteriors a couple of times, (always with super complex models, last time here) and I couldn’t figure out what’s wrong.