I still don’t understand your “infinite limit” idea. If in your post I drop the following paragraph:
A way to think about the proposition Ap is as a kind of limit. When we have little evidence, each bit of evidence has a potentially big impact on our overall probability of a given proposition. But each incremental bit of evidence shifts our beliefs less and less. The proposition Ap can be thought of a shorthand for an infinite collection of evidences Fi where the collection leads to an overall probability of p given to A. This would perhaps explains why the Ap proposition is so strange: we have well-developed intuitions for how “finite” propositions interact, but the characteristic absorbing property of the Ap distribution is more reminiscent of how an infinite object interacts with finite objects.
the rest is standard hierarchical modeling. So even if your words here are suggestive, I don’t understand how to actually connect the idea to calculations/concrete things, even at a vague indicative level. So I guess I’m not actually understanding it.
For example, you could show me a conceptual example where you do something with this which is not standard probabilistic modeling. Or maybe it’s all standard but you get to a solution faster. Or anything where applying the idea produces something different, then I would see how it works.
(Note: I don’t know if you noticed, but De Finetti applies to proper infinite sequences only, not finite ones, people forget this. It is not relevant to the discussion though)
I still don’t understand your “infinite limit” idea. If in your post I drop the following paragraph:
the rest is standard hierarchical modeling. So even if your words here are suggestive, I don’t understand how to actually connect the idea to calculations/concrete things, even at a vague indicative level. So I guess I’m not actually understanding it.
For example, you could show me a conceptual example where you do something with this which is not standard probabilistic modeling. Or maybe it’s all standard but you get to a solution faster. Or anything where applying the idea produces something different, then I would see how it works.
(Note: I don’t know if you noticed, but De Finetti applies to proper infinite sequences only, not finite ones, people forget this. It is not relevant to the discussion though)