That’s how base HMC handles the Metropolis correction (which multinomial-NUTS doesn’t do). Maybe base-NUTS did as well – not a bad assumption.
I dunno if we really know the base set of problems. But fair to ask. Things that are correlated and things that have heavy tails and things that are high dimensional are the standard difficult things from a statistics perspective.
But those problems are sometimes statistics problems, sometimes numeric problems, sometimes adaptation problems, and sometimes coding problems. The issue I have with divergences is it’s hard to get to the bottom of what’s causing them without just guessing. They definitely tell you something is up – but it’s hard to get much else than that from them. Search for threads with “divergences” and you’ll see how shaky our advice is :D.
Here’s a case I think there were divergences cause of a lack of constraints: Divergent transitions in hierarchical logit
Here’s a model you can get to run without divergences if you make adapt_delta really high (but you’ll get them before that): accel_splines.data.R (207.4 KB) accel_splines.stan (2.8 KB)
Here’s a model on the forums where we had to do a non-centering and then a little parameterization change to get rid of divergences: Divergent transitions
Here’s a @betanalpha model where there is funnel behavior but it’s in a weird place: Underdetermined Linear Regression