Thanks for the idea! I didn’t yet find a clear example of how the HMCGibbs work but the documentation seems to suggest to me that I can basically pass samples for some of the parameters to the NUTS optimizer.

Is it necessary that these samples are obtained by Gibbs sampling?

Specifically, I have an ODE system that also contains a few algebraic equations (so its actually a DAE system). To me, it seems like a reasonable (and efficient) approach to sample the parameters in these algebraic equations for each equation independently (as a simple regression), and then pass the corresponding posteriors to the ODE system optimization.

Another reason for doing it like this is that I don’t have much data for some of the variables. So the sampling of some of the algebraic (regression) equations will be based on, for instance, only N=50, while for the ODE variables I have N=500.

I’m definitely also curious to see how well the sampler would work if I pass the posteriors of the parameters in the algebraic equations as a prior to the sampler of the ODE system.