Hi Lily,
I think what you’re trying to do with your nested model is similar to what I was working with in this post and this Colab notebook. In there, I was using the (Latent) GP to model just one parameter in a larger model - I think that’s what you’re trying to do? A key point is you don’t actually use any predict method within the model, you just use the GP itself as the prior on a parameter, and then everything gets estimated simultaneously based on your observations: the GP, the parameter of interest, and all the remaining parameters in your model.
I’m not as familiar with GPs as emulators, though, so I may be misinterpreting your intended workflow.