Ah yes. My very preliminary thoughts were that your (Bayesian prediction) view appears to align more with the Epistemic-Probability-as-Model (EPaM) view in the distinction I linked above. The “superpopulation” use is a way to provide an aleatory interpretation, consistent with the Frequentism-as-Model (FaM) view. Your statement: “We are putting probabilities on parameters to encode uncertainties about whatever particular single values they may have.” is almost a textbook epistemic reading of parameter probability whereby no superpopulation is needed for the inferential framework to be coherent. The key point of course is that both EPaM and FaM are idealizations that do not map perfectly onto reality. Cognitively I have thought much more in terms of FaM (including in my Bayesian modeling) but can see the value of further developing my EPaM muscle. What comes below is an embryonic attempt to do that.
Were I to summarize your position in EPaM terms (let me know if this is correct):
-Parameters are fixed but unknown
-Posteriors quantify subjective uncertainty
-Transportability is a separate scientific judgment about mechanism equivalence
This gives up the automatic license to generalize that comes with the superpopulation framing. Under FaM, if your data is a sample from a superpopulation, you’re automatically making inferences about that superpopulation. Under EPaM, generalization requires a separate argument about mechanism invariance. Whether this is a bug or a feature depends on your philosophy of science. Interestingly, the EPaM view may align with our core thesis here (also touched upon in this thread) that we should be explicit about how we think mechanisms transfer across contexts, rather than having this baked into the probability framework via a superpopulation framing.
So perhaps I may end up continuing using FaM mainly for model building (it just comes naturally to me when making causal inferences from our experimental data etc) but lean more on EPaM for transportability tasks, certainly when making patient-specific inferences in the clinic (that may be my most epistemic domain currently). Or maybe somehow learn to use both simultaneously for all tasks 