Hey,
I just wanted to let you know that I’m working on this and making some progress.
To illustrate this here are some images, without much explanation for the time beeing. Divergences are indicated in red.
8-school model, output of stan:
8-school model, output of my prototype:
Next: the sigmoid-model of the older thread from @martinmodrak :
stan output:
prototype output:
Here we can see that (almost?) all divergent iterations touched the left edge, and that many iterations touched the lower edge without becoming divergent. The lower edge is problematic, too, but apparrently not problematic enought to cause lots of divergences, at least with the settings I used for the sampler here.
The basic idea is that I’m indicating the position of the leapfrog step that contributed the most to the energy error of the integrator. In reality it’s a bit more complicated, though.
For now I’d just like to ask whether there are any particular types of divergence causes or models which you’d like me to use for testing. But please nothing complicated, at the moment it’s more about testing different types of problematic posteriors than complex real world problems. Larger and more complex models would come later.
At the moment I have the two models shown above, a model with a discrete step in the posterior, and a perfectly healthy multivariate gaussian.
Other ideas for testing are models with:
- multimodality
- phase changes (not sure if that is the right term)
- banana or ring shaped posterior
- eventually, something larger and more complex
@martinmodrak: I couldn’t find the code and data for the second sigmoid model that you tested in the old thread. Are they available?