How to “cut” using Stan, if you must

Frederic Bois writes:

We had talked at some point about cutting inference in Stan (that is, for example, calibrating PK parameters in a PK/PD [pharmacokinetic/pharmacodynamic] model with PK data, then calibrating the PD parameters, with fixed, non updated, distributions for the PK parameters). Has that been implemented?

(PK is pharmacokinetic and PD is pharmacodynamic.)

I replied:

This topic has come up before, and I don’t think this “cut” is a good idea. If you want to implement it, I have some ideas of how to do it—basically, you’d first fit model 1 and get posterior simulations, then approx those simulations by a mixture of multivariate normal or t distributions, then use that as a prior for model 2. But I think a better idea is to fit both models at once while allowing the PK parameters to vary, following the general principles of partial pooling as in this paper with Sebastian Weber.

It would be fun to discuss this in the context of a particular example.

I also cc-ed Aki, who wrote:

Instead of parametric distribution a non-parametric would be possible with the approach presented here by Diego Mesquita, Paul Blomstedt, and Samuel Kaski. This could be also used so that PK and PD are fitted separately, but combined afterwards (this is a bit like 1-step EP with a non-parametric distribution).

So, lots of possibilities here.