Differentiating random walk probability w.t.r. rate of jump

[ChrisRackauckas]

@mlanghinrichs

I imagine that stochastic derivatives of the distance function (between model and data statistics) with respect to model parameters would help a lot to explore the parameter space more efficiently. I don’t know, maybe like a Hamiltonian Monte Carlo within ABC, or another form of gradient-based ABC if possible.

Is this something worth to explore? Are you already working on this, or would it be useful to go into this topic a bit? Would be very happy to (roughly) understand the current state of this! The general idea sounds very exciting.

It’s exactly what we’re exploring. That was actually the genesis for the whole project:

Differentiating through a Jump Problem

I took a stab at it, but it turns out to be impossible . The reason is because after doing the rate calculations, you have to arrive at an integer for which jump is going to occur, and that integer value is going to “break” the differentiation chain (duals come out zero), so AD cannot be directly applied here. Mixings don’t seem to make sense. At a more fundamental level, I dug up a Petzold paper that made it a bit more explicit. They took a look at the chemical master equations, and …