Causal networks do not make an iid assumption.
Yeah, I guess that’s way too strong; there are a lot of alternative assumptions also that justify using them.
What is a sample? How do we know two numbers (or other strings) came from the same sample?
I think we just have to assume this problem solved. Whenever we use causal networks in practice, we know what a sample is. You can try to weaken this and see if you still get anything useful, but this is very different then ‘conditioning on time’ as you present in the post.
Since the association contains information separate from the values themselves, how can we incorporate that information into the framework explicitly?
Bayes theorem? If we have a strong enough prior and enough information to reverse-engineer the association reasonably well, then we might be able to learn something. If you’re running a clinical trial and you recorded which drugs were given out, but not to which patients, then you need other information, such as a prior about which side-effects they cause and measurements of side-effects that are associated with specific patients. Otherwise you just don’t have the data necessary to construct the model.
Yes, but this is a completely different matter than your original post. Obviously this is how we should handle this weird state of information that you’re constructing, but it doesn’t have the causal interpretation you give it. You are doing something, but it isn’t causal analysis. Also, in the scenario you describe, you have the association information, so you should be using it.