Would it be possible to see the gradient and every leapfrog of RStan?

[jsocolar]

@RuimingDiao

So it seems only each iteration is saved, not each leapfrog?

Yes, that’s right this saves each iteration, not each leapfrog. That’s why I suggested setting max treedepth to 1, so you’d actually get each leapfrog.

@RuimingDiao

Thanks! I found that interestingly, some chains did not crash into extreme problematic regions after I set max_treedepth = 1, though it went to problematic regions when I set default max_treedepth. Would this imply some possible reasons why my code crashed?

I’ve seen something like this before, and I have a guess (but it’s just a guess) about the behavior. My guess is that when the likelihood surface, far from the typical set, has a steep hill and then a large flat region, the sampler’s initial exploration can send it hurtling down the hill and then out a long way onto the flat region, sort of like riding a sled down a hill and then across a flat field. If the problematic region resides way out on that flat region somewhere, then a large treedepth allows the chain to coast across the flat region far enough to reach the problematic area, whereas a small max treedepth causes the momentum to get resampled before the exploration has a chance to coast too far out onto the flat region.

More discussion of this (hypothetical) phenomenon here:

Offset multiplier initialization

The negative correlation in the centered case is the classic funnel geometry. The global posterior mode in this parameterization sits in the neck of the funnel, but the neck is narrow enough that little posterior mass sits there. In the NCP, my instinct is to search for the cause of the pinch outside of the typical set, because initializations in or near the typical set don’t manifest the pinch. It seems that the key issue somehow involves the interaction between sigma, the random effects vec…