[This seems like a super obvious FAQ, but I can’t find an answer to it because I have no idea what set of keywords would reveal it.]
How do I represent a multi-variable observation process? I’m not sure of the right term for this, so let’s take an example:
What if when I observe some process, I get simultaneous values for variables A, B and C? Put differently, every observation is of the form <a, b, c>?
Is this correctly represented as, for example:
Variable("A", observed=as) Variable("B", observed=bs) Variable("C", observed=cs)
My guess is that the answer is “no”, and the as, bs, and cs above would be taken as independent observations of the three variables.
But in my case, the observations include
(a, b. c), and so forth and
(a[x],b[y],c[z]) is an incorrect observation, in general, unless x = y = z.
In general, also, A, B, and C are not the same type of variables (e.g., A might be
TruncatedNormal, and C
Gamma), so I can’t just make a vector with shapes.
As I said, this seems like an incredibly basic question, but I don’t know how to find an explanation of what it means when multiple variables in a model are observed, or how to make a tuple of observations. I can’t build an observation tuple with a deterministic RV, because I can’t observe a deterministic RV.
Thanks, and apologies for such a basic question.