Is it possible for a parameter to be estimated only using a subset of the data for which the model applies?

Say I have a set of highly reliable measurements of my parameters of interest and I need them to estimate other sets of secondary parameters measured under noisier conditions. Is there a way to use the posteriors from the reliable estimations as fixed for the other sets of noisy estimations within the same Stan program?

(I suppose I could take point estimates from the first phase as inputs for the second one, but that would fail to propagate the small but non-zero uncertainty)

I would estimate both in the same posterior distribution

The correct thing to do is estimate them in the same model like @bgoodri said.

If that’s not easy, then the thing you’re looking for are the measurement error models in Chapter 14 of the 2.17.0 manual. Hope that helps!