I have a general question about priors:

Imagine that i derived a posterior p(f|y) from a previous experiment about a quantity which is function of my new modeling problem f(\theta) . Since theta has a larger dimension the invers f^-1 does not exist. I can not reformulate this posterior as a prior(\theta) analytically.

I guess a statement in stan such as

target += p(f|y)

give my model for the new data implicitly the correct prior probabilities on the \theta manifold?

Has someone counter-arguments on this approach?

Thanks, Jan