I’m not sure if this is something that can be answered by eyeing a plot, but it definitely might be to more experienced people. I have run a multilevel regression and post-stratification model with random intercepts for various demographic features. This plot shows the posterior distributions for one such variable, produced by simply calling ranef() on the model and getting the posterior samples.

I just wondered if this is a ‘normal’ looking posterior. For example, some of them are skewed in one direction or another, and they’re all quite sharply peaked. I think that might be totally normal/desired behavior in the sense that it might represent a tendency to some effect but shrinkage towards the average. However, as I’m used to seeing nice gaussian-looking posteriors, I wondered if this is actually a weird or concerning looking posterior.

The model ran totally fine with no divergent transitions and good ESS. The prior for the random effects was exponential(1) - and I got the same thing with exponential(1.5) and exponential(5).