Multiple shooting analogue for MCMC

[ArnoStrouwen]

Optimization based parameter estimation techniques such as MAP can use state discretization techniques such as multiple shooting to speed up the optimization.
But for MCMC based parameter estimation techniques all examples I've seen use single shooting.

I wonder if using a technique like:
https://arxiv.org/pdf/1702.08446.pdf#page=5
might also work for combined sampling in the state and parameter space, where the manifold is defined by the system dynamics.

[mschauer]

If you have SDEs (a noisy relaxation of your ODE), you can do multiple shooting in MCMC