How would you choose the distributions for the model weights in a way that’s not itself arbitrary? E.g. how do you choose their forms and parameters in a way that’s not arbitrary?
I agree the distributions for the model weights would be arbitrary to some extent. However, I think probability density functions (PDFs) should be precise at a fundamental level, which implies precised expected values (EVs). If 2 PDFs feel exactly as plausible, I would simply use the mean between them.
I am not sure it matters whether one endorses precise EVs or not. In practice, I still like to test different EVs when the underlying PDF is very arbitrary and uncertain, as it is the case for PDFs of welfare ranges. In such cases, I suspect decreasing uncertainty to find the best options has higher EV than the supposedly imprecise EVs of going with the current best option.
On there potentially being no fact of the matter, this may be helpful. It goes further than the issue of imprecise credences/​EVs.
I agree the distributions for the model weights would be arbitrary to some extent. However, I think probability density functions (PDFs) should be precise at a fundamental level, which implies precised expected values (EVs). If 2 PDFs feel exactly as plausible, I would simply use the mean between them.
I am not sure it matters whether one endorses precise EVs or not. In practice, I still like to test different EVs when the underlying PDF is very arbitrary and uncertain, as it is the case for PDFs of welfare ranges. In such cases, I suspect decreasing uncertainty to find the best options has higher EV than the supposedly imprecise EVs of going with the current best option.
Here is a seemingly great summary from Gemini.