How can I effectively propagate parameter uncertainties from one hierarchical level to the next?

[iavicenna]

I have never used the latter approach myself, so not very experienced with it. I have however seen numerous discussions on this which you might find useful:

How best to use a posterior sample as a prior for a future integration in another model?

I am modelling sea-level rise, which is made of various components. I have a model for glaciers contributions, and a model for thermal expansion of the water. I can tune these models separately, independently from each other, because there are observations of glacier retreat, and observations of ocean warming. Using MCMC, I have posterior distributions of the model parameters, and say, of 20th century contribution for both these sources. with pm.Model() as glaciers_model: glacier_param1 = p…

And also this:

Updating priors

It is not exactly your question but also describes using posteriors from previously sampled models as priors for other models, with the help of Interpolated class (for univariate only)